You are in a corner of a 50 ft square room, what is the distance to the center of the room?
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- Опубликовано: 4 мар 2024
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I concur with those that have said that this is a poorly constructed word problem, and I say that as a retired high school math teacher who also worked with students with learning disabilities. I had to learn that in order for students to actually learn something, you have to state problems in the clearest manner possible. I would have written it as "You are in a square room with sides 50" in length". That makes it much more easier to comprehend and visualize, especially since I taught Integrated Algebra and Geometry.
it is not a poorly constructed word problem. It just requires that the student has a working glossary of terms and how to apply them. One could also frame the question so the values need only include the 1/4 of the room the student is standing in. Every technique needed to answer this 'easy' numerical equation is foundational to mathematics. Rejection of extraneous data known as 'simplifying' is second only to accuracy as a goal in Math, the science. Having the mathematical lexicon, the mathematical assignment of variables, the very mathematical steps and how to treat the results. All foundational. All are required in this question. It is not a bad question to ask a student to perform. In your case, you need to constrain how many principles you introduce at a time so not to overwhelm your students. That is tough. But I still wouldn't class this question as difficult. It could have been an isosceles triangle :)
The fact that people are commenting on it is proof enough that it could have been done better@@markanderson3740
Totally disagree with this.
The whole purpose of this very basic applied math, is to map mathematics onto real life and make it useful. If you don't learn basic terminology, you might as well not know anything.
You are not doing kids any favors making things easier for them in school.
Make a mistake like this in real life, and you could show up with insufficient flooring to cover a room and get fired. It could be a life-changing event.
It is probably just as well you retired.
It is poorly constructed. I am German. I understand I am in a 50 foot room that is square. The sentence is nonsensical to me.
@@McGhinchNo, a "50 foot square" would always be a square with sides 50 foot in length.
I thought the question was indicating a square room with an area of 50 square feet!
Hah, ditto!
(can I be excused I've been caged in the metric system for +50 years and English is only my 2nd language?)
This is not how a room would be described in the construction business. This would be called a 250 sq ft room in reality. A better description would have been a square room with a side dimension of 50ft.
@stenovitz
No, just substitute "50m" for "50'". The room will be much bigger but the math will be the same.😂
@@stenovitz
Yes. At least in my language one would never express the size of a room using side length. The size of a (square) roome is expressed in square units, no matter if it is in meters or feet.
By the way;the answer in our case is 10, isn't it?
*5 of course. Forgot to divide by 2.
Why is it that Math Teachers write "confusing"-worded problems with such ease? (Is this a requirement for the job?) At first glance, the phrase "50 ft square room" could be inferred as "a square room with an Area of '50 square feet'."
Actually, that's the difference between saying 50 square feet and 50 feet square. 50 sq ft means an area of 50 sq ft. Whereas 50 ft sq means a square with 50' sides (4 of 'em).
@@terry_willisThat's how I was taught as well. I still remember my Maths teacher explaining the difference. We had the same argument back in the day 😂😂
The same issue I've got and I couldn't understand what is all that talking about...
Such I was thinking a^2=50 and 2•a^2=c^2 => 2•50=c^2, 100=c^2 => c=±10
such c/2=5 ft. (while: a=√50=5•√2=~6.05) 😄
Do is not the correct answer, are you one atom wide?
@@terry_willis, Much thanks!!!
I thought at first you were saying a room of 50 square feet, which I was able to quickly solve for 5 in my head!
If the room is 50 square feet you don't have enough information to solve it. You don't know what shape the room is. If the room has four sides 7.07 feet then you are correct but what if the room is not square.
@@joelethridge3020Well actually the wording does say "square room"
35.355 Answer is D. 35.4 ft ... Because the diagnal of any square is multiplied by 1.4142 ... So 50 x 1.4142 = 70.71 divide that by 2 = 35.355
I assumed the room was 50 square feet. 🙄
You are not the only one. Very ambiguous question.
That would only be true if "foot squares" was a thing, which it isn't.
At the title card (0:02), my answer is d) 35.4'.
To find the distance to the center, we use the Pythagorean Theorem, where A^2 + B^2 = C^2 (the hypoteneuse).
Getting to the center means we're walking the hypoteneuse of a right triangle with the other 2 sides each being half the distance along the walls, so 25' each.
25^2 = 625, and 625 + 625 = 1250.
And thus, SQRT(1250) = ~35.4' (35.355339.....).
Yes, that's what I used and you can pretty much do this in your head.
Distance from corner to corner is the hypotenuse of a right triangle with two adjacent sides 50ft. Pythagoras gives the length of this hypotenuse as sq rt (2500 + 2500) = sq rt 5000, or a little over 70 ft. The centre of the room will be exactly halfway along this hypotenuse, so the answer must be over 35 ft and only d) satisfies this condition.
A 50 ft square room is absolutely a room that has sides 7.07ft long ( sq root of 50). Any house plan has room areas designated in square footage or meters. The room featured her going by the wordage is actually 2500ft square. Nice! Bit of a hike to the centre.
I understood it perfectly fine. Now maybe somebody might say 25' because they thought "to the center" meant center of a side. BUT the title of the video did say "center of the room".
Mr. Mathman,, is there a rule for how we say this? 50 sq. ft room or 50 ft square room. So it should be clarified as to what the meaning is. OR which is it? A 250 sq ft room made all the answers seem way off for a none of these answer. But it may be we are expected to know the difference as to which statement describes 2500 sq ft. Small scrunchy face.
There is nothing in the wording that implies square-footage. It is only ones own biases that would make that assumption. Take the description one word at a time. You have a room. It is a square (all 90* angles and equal sides). Those sides are 50 feet.
Questions like this are supposed to be challenging.
@@retiredump7038 that little mark just after 50 at the top of it says feet
50 foot square is a square with 50 foot sides. Otherwise it would say 50 square foot.
@@retiredump7038
Well said!
Several commenters have stated that the diagonal of a square is approximately 1.41 times The length of anyone of the four sides. Or that the hypotenuse is 1.4142 times1 of your two sides.
I don’t remember learning this arbitrary number 1.4142 in school however, if you consider what everyone already knows about the Pythagorean Theorem and you know you’re talking about a square with four equal sides
You can actually calculate it in this way you know that C Squared is equal to A squared plus A squared Or C squared is equal to B squared plus B squared. The sides are actually interchangeable because they are equal
And instead of dividing by two, we know that we can multiply by .5 which is 1/2.
So if you will take the square root of .5 you will get .7071 As you scroll through the comments, you will see this number expressed over and over again and quite a few of the comments
Because it’s not as easy to square numbers in your head, this is a number that I’ve memorized for a long time when dealing with squares It’s much easier to multiply the hypotenuse by .7071 which is basically 70% of the hypotenuse length when dealing with a square
You can easily reply 50×.7 and get 35 and again moving the decimal over to places 71×50 would be again .355
So just remember .7071 or almost 71% and when you see problems like this on a test and you only have to approximate or guess the closest answer it might save you a few steps to just multiply that number times the diagonal or the hypotenuse
I did it by what is half the square root of (50^2 + 50^2) - so half the square root of 2500 + 2500 or half the square root of 5000; now the square root of 5000 is the same as square root of (50 x 100) or the (square root of 50) x 10; square root of 50 is 7.'something' (7^2 is 49, so we know sq rt of 50 must be just over 7); so sq rt of 5000 is going to be 70-something and finally answer will be half of that; since the multiple choice answers have only one that is applicable as being > 35, we know that d - 35.4 is the right one. Final check with calculator shows (sq rt 5000)/2 indeed = 35.355 or 35.4 to one decimal place
Divide the square into equal quarters. Draw a segment from the center of the original square to a corner. This diagonal divides one quarter and is the hypotenuse of the two resulting triangles, each with remaining sides of 25’ each. Using the Pythagorean Theorem, the length of the diagonal is sqrt1250 or approximately 35.36 ft, so d.
I solved this problem by using the law of sin and cos. Given that the shape is a square, when you create the diagonal, you create a 45-degree angle. By taking either the sin or cos of the 45-degree angle and using either the length of the adjacent or opposite side as appropriate, you can calculate the length of the hypotonus. Then divide the hypotonus in half to calculate the distance to the center.
A 50' square room is 50'W x 50'L.
The center of the room is half the distance along the width & half the distance along the length.
That forms a triangle that can be solved with Pythagoras theorem: a² + b² = c²
So: sqrt (25² + 25²) = c = ~35.4 ft (i.e. a straight line from the corner of the room to the center of the room).
Depends upon what "50 ft square" means.
10 x 10 is 100 sq ft
So 5x 10= 50 sq ft
D. This is actually worded fine, I only had to read it once to know what was being described.
sqrt(50^2 + 50^2) / 2 = ~35.4 rounded to tenths
The corner-to-corner diagonal of any square is approximately 1.414 times the length of a side. The midpoint of the diagonal is the center of the square, so the distance from a corner to the center would be 0.707 times the length of a side. In this problem 0.707 × 50 = 35.35
To better understand the concept, take a 1 by 1 square, divide it with a diagonal and use the Pythagorean Therom to find the hypotenuse cum diagonal.
Or, (√2 X 50)÷2 = 35.36 (2d.p.) This is a very badly written maths problem. It should have been made more obvious what was required.
I worked it similar to that... But I only need !/2 way down one side and i/2 down the other side to get a center point... So I used 25 as the number of A and 25 as the number of b so that 25 squared is 625 + 625 = c squared =1250 the square root of 1250= 35.35
The square of 50 = 2500. Square root of 5000 = 70.7 = the length of the diagonal of the room. From the corner to the center of the room is half the length of the diagonal
i.e. 70.7 divided by 2 = 35.4
The distance to the center of a square from the corner is 1/2 Swrt(2) * Side. D) 35.4 is the answer. This comes from the Pythagorean Theorem: finding the Hypotenuse of the right triangle that created by the points: Center, Corner, Side Midpoint. This is aa 1/1/Swrt(2) standard right triangle. So you multiply Sqrt(2) * 1/2 Side length.
Misleading wording. Implies different than how you calculated
Quickly in head-equal sided triangle- sides 1, 1, sq rt 2. =1.4 by 1/2=.7x50=35 Answer only can be D.
working out a quick estimate system for right triangles. where 'a=b' multiply the length of 'a' by 2/5 and add that amount to 'b' to find 'c'. not sure yet if it is easier :)
seems to loose relevance as 'a' approaches 100. works best for smaller values. edit: i take that back, it's still within 1% at a=898 and seems to continue to be 'lowball' by 1% of the total.
if I added a step of complexity to my shortcut I would add the first significant digit(s) of the estimate to itself (the 1 of 123), using all digits down to the 100's (the 12 of 1234 or 123 of 12345), then my estimate is within 0.1% or less. hmm, is this already a thing?
c~1.01(2/5a+b) how is that? :)
Way to do a quick estimate using similar triangles: instead of triangle with legs 25x25 and having to figure out square root of 1250, do a 5x5 triangle instead and multply that answer by 5, so 5^2 +5^2 = 50, square root of 49 is 7, so square root of 50 is roughly 7.1, now multiply by 5 and the length to center is 35.5 roughly quick close enough estimate to solve a multiple choice question without large numbers or a calculator.
4:49 just make a triangle. So:
A^2 +b^2 = c^2
Ergo
50^2 + 50^2 = c^2
5000 = c^2
Sqr (5000) = c
So that is 70.71.
To find the middle just divide by
70.71/2 = 35.35 or rounded 35.4
I prefer the 2nd solution...thnx...
Square = 4 triangles w 2 equal sides ( x) & hypotenuse = 50. 50 squared= 2500. 2xsqd = 2500.
xsq =1250. Sq root of 1250 = 35.36
If u don’t know that rule about 50 square root of 2. Can u use Pythagoras?
draw a 5" square measure the diagonal and halve it :just over 7" is 35.4
Worked in aerospace for years. The sin of 45 is .707, if you only remember one trig value this is it.
About 18 seconds, not 18 minutes.
1) Diagonal = 50*1,4 (ca sqrt of 2)= about less than 75
2) diagonal/2 = about 80/2=about 35
First I was not confused by the language. It's obvious to me he means a square with 50 sides not 50 square feet. I simply used my calculator to find the square root of 5,000. 35.35.
I hesitated at the first reading but after reading it several times, there could be no confusion between foot square (as stated) and square foot. And English isn’t my first language…
The woeding is vage and ambiguous, "a 50 ft square room" I took it as 1) the room is square 2) its area is 50 ft.
Was it too hatd to explicitely word out that the side was 50 ft ??
hmm, I get 35 feet 4-1/4 inches. Because to an interior decorator, "Point Four Feet" makes no sense; tape measures aren't divided into decimal feet, but rather they are divided into inches. But nonetheless, with that said, I'm guessing "D" is probably the answer he is looking for here.
I cheated and did it in my head. Either I was lucky or I got it by a coincidence. OK, I’m assuming you mean that each side is 50’. Either way, I used the P.T., as you did, but I figured that since it’s a square room then a = b. Then, I said a = 1, which means b = 1. That would mean that 1 squared (which equals 1) plus 1 squared (which still equals 1) equals 2. The square root of 2 is roughly 1.414. (I know that from my old days as an electronic engineer.) so, 1.414 X 50 is roughly 70.7, and half of that is roughly 35.3.
The most interesting part starts at 14:52.
The problem is well stated. 50' square means 50 feet all four sides. Don't skim read the problem and misread it as 50 square feet. 25 sqrt(2)=
25 × 1.414=
It's a muktiple choice problem, call it 25 × 1.4= 35
Take the closest answer
Diagonal of a 50' square is 50V2 and half of that (corner-center) is 25V2' and that is the exact answer. But then there are these stupid multiple choice answers so we will need to find the decimal...
Without a calculator this is quite a challenge because of the irrational. But since multiple choice is stupid, we don't have to be accurate and can simplify to V2 = 1.4 and a little bit (instead of 1.414....)
So 25 x 1.4 = 50 x 0.7 = 100 x 0.35 = 35' and a little bit... and that is close enough to answer D.
I prefer 25V2' !
I don't get the confusion in the comments. 50 units square is a square with sides 50 units long. 50 square units wold be the area.
John, you need to better describe what you mean by 50 ft square. Is it 50 ft on each side or 50 ft around the perimeter?
Rooms are described as ... length by width. Example 20' x 16'. When it is a square room, then you only need the dimension of one wall = 50'. Rooms are *not* described by their perimeter.
35.4
D 35.4.
Mental arithmetic in 10 seconds: Scale each side to 5 ft (instead of 50). Diagonal is thus √ 50 (Pythagoras) ≈ 7 x 10 (scale factor) ≈ 70. So semi-diagonal ≈ 35 i.e. 35.4 Teachers should teach imagination and insight not just rules.
Woo hoo...got 35.4.
Isoselese tri with a 50 hyp.
Each side is 35.4.
Thanks for the fun.
35.4’ a square +b square = c square
D 35.4
Therefore d) is the answer
where have the multiple stars gone? I only see a A+ a 100% and a happy face. I miss them.
Easier to do without a calculator if you draw the triangle as 25’ by 25’ to the center, then calculate the hypotenuse.
50x1.414/2=35.35
Question is to stump you using words in lieu of math. Most math instructors are bored, they have a difficult time communicating with people and students bc they are very concrete sequential.
If the room is a perfect square, then the answer is 50 feet/✓2 = 25✓2 feet
If the room is not a perfect square (rectangle, oval, irregular, etc.), then more information is needed.
No wonder some students breezed through their SATs... They knew the shortcuts! Not me though...
The room shown is 2500ftsq (50' x 50'). It is not "50 square feet".
That's probably why it says "50 foot square"
Pythagorus Theorum
Unless you are infinitely thin it can’t be D so C is the most reasonable answer.
Assuming the room is a standard 8' tall, the distance from the corner to the center is 35.63'
I calculated based on a ceiling height of 50', got a corner to centre of room (not just centre of floor, which is what seems to be meant here) distance of 43.30127019'.
25'
Almost 60 and I'm here for my A+, 100%, happy face, and certificate 😂
The length of the side of a 50-foot square room is 7.07 feet.
It does not say ... "square feet"
sqrt(5000)/2
(√(50²+50²))÷2
35.4 feet yes
I know this is math class, not English (although kids today are failing both and still managing to graduate high school), but you mean 50 square foot room.
you often say dont use a calculator but the square root of 2 at 1.414 is burned into my brain for the past 35 years
My only complaint is I thought it was a 50 square foot square area. Should said 200 ft perimeter or that each side of square is 50 ft . Use English.😊
a) 25
If it was 50 square feet, none of the answers would be correct. So it becomes obvious that it must mean a side that is 50 feet. Still should have been clearer, but it is no excuse to miss it since the possible answers clear up the ambiguity.
i would never point out to a teacher that he was wrong🤣 but you mean a 2500 sq ft room
Yes, a 50' square room contains 2,500 sq ft. But no, we do *not* care about the square feet.
@@MrSummitville YOU CAN'T TELL A OLD RETIRE CONCRETE CARPENTER 50 SQ FT MAYBE YOUR QUESTION SHOULD HAVE BEEN A ROOM 50FT BY 50FT ONCE YOU SAID SQUARE THAT THERE IS THE PROBLEM
@@ronaldmillier9484 Nobody said. "50 sq ft". You made that up.
@@MrSummitville A word problem is any math problem based mostly or entirely on a written description OK I WILL GO SIT IN THE CORNER WITH MY DUNCE CAP ON BUT I THINK THERE IS MORE THAN ONE PERSON IN THE CORNER THAT SAW SQUARE AND CONCLUDED SQ FT(working over 50 years in sq ft) THANK GOD THEY HAVE BLUEPRINTS IF IT WAS ALL WORD PROBLEM : (
25
25 × √2 = 35.4
D
The wording is wrong! The area of the room is 50 sq ft. Area=Length X Width e.g. (10' x5' = 50 sq').
The answer is d
You are wrong, Einstein. 50' square room is 7.07 x 7.07. So 7.07 x 1.41 = 10. Then 10/2 = the correct answer. 5
No, he did *not* say, the room contained 50 *square* feet. Your assumption is very wrong.
It is not 50 ft sqr, 2500 square feet instead!
For 50 ft sqr, result is 5'.
No that's 50 sq ft. Word order is significant. Just like 30 lb/in is not torque, but 30 in/lb is.
D This was hard.
Got it quick... and im an old dumbass 😂
This one had to be easy. He didn't say, "Most Will Get This Wrong".
B
D, because I was always told that the diagonal of a square was ≈ to 1.5 times its side, so I picked the one that was closest to the approximate answer (75/2 = 37.5 ≈ 35.4). Of course you could do the Pythagorean Theorem and get the exact answer, but that takes too much time.
A
Square feet and feet square are two entirely different concepts. Join the normal world.
Distance=√1250
a
A 50ft square room has sides 7.071feet in length (7.071 x 7.071 = 50 ft). The square root of (7.071x7.071*2) divided by 2 = approx 5 feet.
a 2500 sq ft room would be pretty big! Don't know if I'd call that a regular room.
50 foot square is not 50 square feet thus it is not speaking area
I thought 50 was the area of the square
The question is unclear. What distance to the centre is being sought? The distance from corner, from the middle of one side………Better would be…”How far are you from the centre of the room?”
2500 sq room
This problem is incorrectly solved according to the way it’s worded. A 50’ square room implies that the area of the room is 50 square feet.
50 square feet or 50 foot square need to better define problem. High school students will be confused.
d,
Exactly the same bad wording as the 40ft square room version you posted 4 months ago.
here is another DEFINITION sensitive question...
50 square feet
and
50 feet square
ARE DIFFERENT
"50' SQUARE" IS 50'×50'
Being square the diagonal is at 45° at corner with triangle ratios 1:1:sqrt(2)
The diagonal here is
= 50'×sqrt(2)
= 50 × 1.414
= 70.70
half diagonal is
= (1/2)70.70
= 35.35
50x50=2500+2500=5000. Sq rt of 5000 = 70.710678. 1/2 of that = 35.355339. None of the multiple choice answers is correct. And it matters not plus over minus nonsense this dude spewed out to obfuscate and confuse you.
People and science and mathematics generally use the metric system?
Americans are certainly their own kind of people??
One example is how 3 grams of creatine should be taken; 121-200 pounds?? WTF
Doh. I recalled √2 as ~1.212 and came up with ~30.
how close to the corner can you stand ? If you can stand 35.4 feet from the centre you are some contortionist ! How about 35' less a bit !