How exciting indeed. I’ve been watching your videos for a few months now for entertainment but never had the courage to attempt any of the problems myself. I decided to give this one a go. I had the widest smile on my face seeing my numbers the same as yours as I rewatched the video. I’m currently in highschool geometry and you help me think outside the box for problems like these.
I over-complicated it, but I still like the picture I drew. Because these are right triangles and the known bit of each edge is 6, I can copy this shape 4 times, arrange it as a square with side 13x and an interior square whose edge is the hypotenuse of the white triangle. Subtract the big square from the small square, divide by 4 to account for my copies, and I get 21x² for the area of the red region. Of course, to solve for 'x' , I subtracted the small triangle from the big triangle and set it equal to 21x² and blinked and was like... oh.
It's funny how you guys call an expression like ax2+bx+c=0 "quadratic" whereas in Spain we use that term for ax4+bx2+c=0. We call the former expression "2nd degree" instead.
It is 2nd degree and what you comment is 4th degree or quartic! Quadratic is from Latin - quadrare - to square. So involving terms of the second degree at most.
it just clicked why an area of a right triangle is base * height divided by 2. Cuz its literally just half a square.. it took me too far long to understand that and now the logic behind all sorts of equations are starting to make sense
I can’t tell you how excited I am. I did everything until the quadratic equation then I fed it into an online quadratic formula calculator to get x=2/x=-3/7 because I’m lazy.
Thanks to the memoriation based teaching methods which are commonly used here in Turkey, everybody who had to deal with geometry, tries their luck with 5 12 13 triangle as soon as they see the number 13. Checking if it fits or not, takes 2 or 3 seconds. If it fits, 8 or 10 more seconds is enough to solve the rest. So, total time for this question is about 15 - 20 seconds. We have to finish it in that time in order to gain more time for harder stuff. I don't know if it's something good or not. I am watching Indian people math questions on youtube sometimes. They are hardly given nice numbers such as 3-4-5 or 5-12-13 or 8-15-17 or 7-24-25 or 9-40-41. Yep, my brain is cursed too.
This is easily solved much faster with a Pythagorean triad 13,12,5. 12x - 9x =3x 3x =6 x=2. Alternatively 5x-2x=3x 3x=6 x=2 Areas- total = 12x5/2=30 white =9x2/2=9 red =30-9=21. So much simpler
I got scared when the numbers were in the triple digits but after taking the -12 (I didn't realize they were all divisible by 12 until after I took out -1, 2, 2, 3 lol), it came down to one of my favourite things in math, factoring! How exciting :)
The area of the red region is equal to the area of the larger triangle substracted from the area of the smaller triangle. The area of a triangle is equal to base*height/2. For right triangles, we already know the height, which is the length of the side perpendicular to the base. Using the given information, we can construct an expression for the area of the red region. The area of the larger triangle is equal to (2x+6)(9x+6)/2. The area of the smaller triangle is equal to (2x)(9x). Expanding the products, substracting them and then 3(11x+6), which is the area of the red region.
@@oat.s.s: He forgot to mention it, but he did it for the final answer, which is indeed 33x + 18, or as he writes it, 3(11x + 6). No idea why the problem statement even mentions the 13x in the hypotenuse, since it's not necessary at all.
@@hoon_sol The hypotenuse is needed indeed. By doing it as @Fire_Axus you just solve it as a function of x, not as an explicit value. Think about it - if you weren't given a hypotenuse you could choose x as you want want the triangle would change shape. With it given the proportions of the catheti are unambiguous.
I didn't use the quadratic equation because it can be factored into rational numbers: (7x-3)(X-2). If you do -6 * 7 = -42 and recognize it's factors -14 and 3 add to be -11, it's straightforward from there.
That moment when he shows (a+b)^2 = (a+b)(a+b) instead of as a^2 +2ab +b^2 and then proceeds to simplify to the end but then does not do the same for the values of x and leaves it to the viewer to calculate the root and directly gives the answer of x = 2, -3/7
Using the Pythagorean theorem you find the value of X, and then you find the area of the smaller white triangle, then subtract it from the big red triangle an you get the answer.
Bah. No need to use the quadratic formula. 7*-6=-42, and 42=2*3*7, so you can pick -14 and 3. Then rewrite the equation as 7x²-14x+3x-6=0 and factor by grouping. 7x(x-2) + 3(x-2) = (7x+3)(x-2) = 0 The first factor will be negative, so just take x=2.
I don't think that I can praise your videos enough. Simple and straight into the problem while showing a bit of humor. Fantastic work.
Myself from 2 decades ago wouldn't have ever imagine myself today watching someone solving math problem as a therapeutic sesion.
I wasn't even alive 2 decades ago but I have the same feelings
Quite simple but quiteeeee exciting!!
True
How exiting
Howwwww
How exciting indeed. I’ve been watching your videos for a few months now for entertainment but never had the courage to attempt any of the problems myself. I decided to give this one a go. I had the widest smile on my face seeing my numbers the same as yours as I rewatched the video. I’m currently in highschool geometry and you help me think outside the box for problems like these.
I love it!
I like how you solve problems. You choose not hard ones, but interesting ones
I love how math turns a simple question with numbers and letters into a BIG Equation into another equation into a simple answer
I swear, these are the best math videos around. awesome job. I'm smiling like a kid at the end of these. How exciting indeed!
I love how youtube suggested this channel, but hasn't suggested ANYTHING else, math related! unique content, dude! lovely work!
i love your videos so much, they make me so excited about math
A simple one to reinvigorate me after failures on your previous ones. Nice!
Dude....are you some kind of math genius or something? Every one of your videos impress me....and reminds me how much I've forgotten.
I love your channel
Yet again great video. very easy to understand explanation.
After many years, i still can solve it 🎉
wow these are great problems, easy enough and simple yet interesting and get you to think a bit
169
Nice
😂😂😂😂
These are the best video's, and on top of that the add is at the end. Thank you.
im from brazil and i love your content
I'm from Belarus, and i also love your content
im from brunei and i love your content also@@simonoleksin6352
@@simonoleksin6352wait you love the content of pedrog?? 😮
Dale Brasil!
You could have uses the "complete the square" method when solving the quadratic problem, and I find this method easy and great to use.
Last time I used maths was 2016, and I managed to solve this with the correct procedure, proud of myself
How exciting!
You know something’s more important than you can even imagine when he puts a box around it and it’s not even the answer. How exciting.
You’re very kind to throw us a few softball now and again so we don’t feel too dumb 😅
I over-complicated it, but I still like the picture I drew. Because these are right triangles and the known bit of each edge is 6, I can copy this shape 4 times, arrange it as a square with side 13x and an interior square whose edge is the hypotenuse of the white triangle. Subtract the big square from the small square, divide by 4 to account for my copies, and I get 21x² for the area of the red region.
Of course, to solve for 'x' , I subtracted the small triangle from the big triangle and set it equal to 21x² and blinked and was like... oh.
NICE
2:00 - "Hy-pot-ten-noose" 🤣
I got “33x+18” and thought I was done 😂
It's funny how you guys call an expression like ax2+bx+c=0 "quadratic" whereas in Spain we use that term for ax4+bx2+c=0. We call the former expression "2nd degree" instead.
It is 2nd degree and what you comment is 4th degree or quartic! Quadratic is from Latin - quadrare - to square. So involving terms of the second degree at most.
how exciting
it just clicked why an area of a right triangle is base * height divided by 2. Cuz its literally just half a square.. it took me too far long to understand that and now the logic behind all sorts of equations are starting to make sense
nice but i did this by hit and trial, Pythagorean triplets
How exciting
I can’t tell you how excited I am.
I did everything until the quadratic equation then I fed it into an online quadratic formula calculator to get x=2/x=-3/7 because I’m lazy.
Thanks to the memoriation based teaching methods which are commonly used here in Turkey, everybody who had to deal with geometry, tries their luck with 5 12 13 triangle as soon as they see the number 13. Checking if it fits or not, takes 2 or 3 seconds. If it fits, 8 or 10 more seconds is enough to solve the rest. So, total time for this question is about 15 - 20 seconds. We have to finish it in that time in order to gain more time for harder stuff. I don't know if it's something good or not. I am watching Indian people math questions on youtube sometimes. They are hardly given nice numbers such as 3-4-5 or 5-12-13 or 8-15-17 or 7-24-25 or 9-40-41. Yep, my brain is cursed too.
This is easily solved much faster with a Pythagorean triad 13,12,5. 12x - 9x =3x 3x =6 x=2. Alternatively 5x-2x=3x 3x=6 x=2 Areas- total = 12x5/2=30 white =9x2/2=9 red =30-9=21. So much simpler
How exciting 🎉
I got scared when the numbers were in the triple digits but after taking the -12 (I didn't realize they were all divisible by 12 until after I took out -1, 2, 2, 3 lol), it came down to one of my favourite things in math, factoring! How exciting :)
Howw exciting...!!
The area of the red region is equal to the area of the larger triangle substracted from the area of the smaller triangle. The area of a triangle is equal to base*height/2. For right triangles, we already know the height, which is the length of the side perpendicular to the base. Using the given information, we can construct an expression for the area of the red region. The area of the larger triangle is equal to (2x+6)(9x+6)/2. The area of the smaller triangle is equal to (2x)(9x). Expanding the products, substracting them and then 3(11x+6), which is the area of the red region.
Bonus: Substituting x for 2 gives the area of 84.
you forgot to divide the (2x)(9x) by 2
@@oat.s.s:
He forgot to mention it, but he did it for the final answer, which is indeed 33x + 18, or as he writes it, 3(11x + 6).
No idea why the problem statement even mentions the 13x in the hypotenuse, since it's not necessary at all.
@@hoon_sol The hypotenuse is needed indeed. By doing it as @Fire_Axus you just solve it as a function of x, not as an explicit value. Think about it - if you weren't given a hypotenuse you could choose x as you want want the triangle would change shape. With it given the proportions of the catheti are unambiguous.
stop saying how excited but very cool trick
“And we can’t have a negative hypotenuse.”
I didn't use the quadratic equation because it can be factored into rational numbers: (7x-3)(X-2). If you do -6 * 7 = -42 and recognize it's factors -14 and 3 add to be -11, it's straightforward from there.
That moment when he shows (a+b)^2 = (a+b)(a+b) instead of as a^2 +2ab +b^2 and then proceeds to simplify to the end but then does not do the same for the values of x and leaves it to the viewer to calculate the root and directly gives the answer of x = 2, -3/7
one sixty-nine... nice!
First one I’ve been able to solve!! I don’t care if it’s easier I feel awesome 🎉
기막힌 보조선을 기대했는데... 그냥 대수적인 계산이었네
how did you learn this? Is it just memorization of a specific problem?
What's there to learn?
No. They just learn the basics of geometry and start solving based on what they have learned. Its not memorizing problems, but memorizing theorems
Its all about problem solving skills. Using the tools of math to work your way through.
You could have found the difference before solving for X, that way you have only the equation ahead.
Using the Pythagorean theorem you find the value of X, and then you find the area of the smaller white triangle, then subtract it from the big red triangle an you get the answer.
yep, looks like I was right.
Only nerds say “how exciting!” after solving a geometry problem. 😂
Finally. A question I can solve.
pretty simple problem. Though i factored instead of quadratic which i got (7x + 3)(x -2) = 0
Absolutely
I finally got one of these! 🤗
Özel üçgenler de arayabilirsiniz.X,2 için 10 24 26 özel üçgeni gelir
Found 168, let's see if I'm correct.
EDIT: forgot to divide by 2 for the areas so it's actually 84.
2:03 2:04 hyPOteNUse
highpotenuses are never negative
0:41 WHAT?
finally a question i can solve
Almost.
Gyatt it
I simply put x as 1 and 2 and got a pythagorus triplet
HOLY CRAP I FINALLY SOLVED ONE WITHOUT WATCHING THE VIDEO!!!!
169 NICE!
2x,6x,8x its side of the triangle so how find value of x
ez
Hypot tah noose
I tried to find x... I wouldn't want to recomend.
nvm I got it!!!! didn't think that I would get it lol I thought there was a super esaier way.
0:26 Which theorem ? 💀
?
good old Pythagorean Theorem
@@259 yeah I dunno what he's trying to say
Bah. No need to use the quadratic formula. 7*-6=-42, and 42=2*3*7, so you can pick -14 and 3.
Then rewrite the equation as
7x²-14x+3x-6=0 and factor by grouping.
7x(x-2) + 3(x-2) = (7x+3)(x-2) = 0
The first factor will be negative, so just take x=2.
Isnt it 168?
Happened to me. Do not forget to divide by 2 for the triangle areas.
A_shaded=84
First again! Woo hoo
Damn bro just try giving x the value of 2. It is obvious that it is just a 5,12,13 triangle.
Too easy, takes 30 seconds by looking.
How exciting
How exciting