Can you find the Area of the Yellow Rectangle? | Fast & Easy Explanation
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- Опубликовано: 9 сен 2024
- Learn how to find the area of the yellow region. Step-by-step tutorial by PreMath.com
#OlympiadMathematics #OlympiadPreparation #CollegeEntranceExam
Well done! The simplest things are often the most beautiful. Greetings fro Italy!
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Unknown area should be proportional to both left and right areas as increasing or decreasing it also effect the right and left areas at same proportions.
So, in order to express the proportions on an equation, we need to solve this:
(29 + A) / 9 = (43 + A) / 11
Hence A = 34...
No need to take account the "y" value mentioned in the video as its insignificant or unrelated for the solution.
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this was another gr8 solution..seriously man..the level of imagination i posses seems to b at a pretty low level...
Great problem! There's definitely a few ways to go about it. I set up a system of equations where x=the width of the yellow region and y=the height of the yellow region. Equation for area of the green region: (9-x)y = 29. Equation for pink region: (11-x)y = 43.
These two equations are my system of equations. Solve the green equation for y: y = 29 / (9-x). Then substitute for y into the pink equation: (11-x)29 / (9-x) = 43. Simplification yields x = 68/14 = 34/7. Now that x is known, use it to solve for y: y=7. Now that we know x and y, the area of the yellow region is: Area = xy = (34/7)7 = 34.
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Same way I worked it. 😀
Similar. I used the same two equations, but muliplied out the brackets and rearranged one to be '-xy = ... ' this allowed me to get rid of the only x term and so i solved for y first. I ended up having to cross multiply 11 - (43/7), to get 34/7 and realised at that point only (😬) that the 7 would cancel out.
After learning the overlapping rectangles in a previous video, I found this easy.
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I did this:
43 - 29 = 14
We know that 11 - the red width = 9 - the green width
11 - 9 = 2
So the area is different from 14 and the two widths are 2:
14/2 = 7
So we have the length of the three rectangles.
Then we calculate the width of the red rectangle = 43/7
So we have the width of the yellow rectangle = 11 - 43/7
Multiply the result by the length = 7
(11 - 43/7) x 7 = 77 - 43 = 34
I used to do math, just for fun. Now I remember why. Thanks from an older person.
Before watching: The height of the object is 7 and the area is 34. (9-x)*h=29 and (11-x)*h=43 leads to h=7, x=34/7, thus the yellow area is 34 square units.
The same way I did it. However, like the professor’s better.
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Easy question!! For the 1st time, i was able to solve ur question without help!!!
A= yellow area, y = height, 9y = 29+A, 11y = A+43, then y=7 & A= 34
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I took it that the ratio of the areas of (green + yellow) to (pink + yellow) is 9 : 11.
So ( 29 + A ) / (43 + A ) = 9 / 11
Cross multiplying 9 ( 43 + A ) = 11 ( 29 + A )
387 + 9A = 319 + 11A
68 = 2A
34 = A
And I wrote the sides of the right rectangle y and 43/y . The left one y , 29/y .... The yellow one is y over x ... Two simple equations ...
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I liked your yesterday's video and felt very relaxed after watching that amazing masterpiece. I want you to make several videos of that type as I love algebra.
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Am greeting from Syria for all your interesting problems solution...
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We decide on the fingers. We chop off the area difference from red with green, equal to 14. Obviously, the width of green + yellow will also be 9. It took two units of length and 14 units of area. The price of a unit of length in units of area will be 7. Everything else is arithmetic for a first grader.
Thanks sir. Because this puzzle did not solve also my maths teacher. 🔥
Lovely explanation, I did it with linear equations with two variables.😅 Got the answer and your way is just amazing
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Before watching:
Let h = the height of the entire figure
Let A = the area of the yellow part
Then
11h=43+A
9h=29+A
---‐---‐--------- -
2h = 14
h=7
Now, let x be the width of the yellow part. Then
11=x+y
With y the width of the pink part.
Now, y= 43/7
So 11 = 43/7 + x
x=11 - 43/7 = (77-43)/7 =34/7
A=34/7*h=34/7*7=34
After watching: also good.
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I got 34/7 for the missing horizontal measurement after getting 7 for the vertical measurement and thought I had done something wrong, then I multiplied length by width and got 34 square units. I spent time looking for a mistake before finally multiplying length x width to get the area of the middle rectangle which was the question being asked by the problem.
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Your tuition is working - I got it right! Thank you so much
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Excellent solution more of these geometry problems please
Looked like a geometry question. Solved it with algebra.
I got it right 60 years later.thanks
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My pleasure!
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Sir As l had been watching your videos regularly l was able to solve it by myself. Thank yous lot
Very good Niru dear
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Great explanation👍👍
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Here's my take:
Green region = s*a = 29
Yellow region = s*b = A
Pink region = s*c = 43
s[(b+c) - (a+b)] = s(11 - 9) = 14
s = 7
so, we have A = 7*9 - 29 = 34
I used the same method, it took about 30 seconds.
wow..this was a gr8 solution
Let the base of Yellow Rectangle be x & height of the Recangle be h.
(9-x)*h = 29 & (11-x)*h = 43, Subtract these to get 2h = 14 So h = 7
Put that value into anyone to get xh the area = 34. ( 63 - xh = 29, xh = 63 - 29 = 34; 77 - xh = 43, xh = 77 -43 = 34 )
Easy question, thanks for sharing
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Super problem ! I enjoy it 🙂
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Thanks for video. Good luck!!!!!!
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Yes I found it. It is the region bounded by black, with the yellow interior. That wasn't hard. Find means to recognize or discover (something) to be present. Your title didn't say anything about computing the area of it.
Solution of the proportion (29+x):(43+x)=9:11 is x=34
Just position green rectangle over pink, just adjacent to yellow.
Решаем на пальцах. Отрубаем от красного разницу площади с зелёным, равную 14. Очевидно ширина зелёного + желтого станет тоже 9. Ушло две единицы длины и 14 единиц площади. Цена единицы длины в единицах площади будет 7. Всё остальное арифметика для первоклассника.
Ans : 34 square unit
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34 sq unit solved very easily
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Excelente
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very well demonstrated bro, thanks for sharing this area problem
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Thanku
Sehr schön danke
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nice!
the design does not respect the relationships between the areas indicated otherwise for example the base of the triangle of indicated area 4 would be equal to double the base of the triangle of indicated area 1
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Good math
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You can solve a 3 equation system (a,b,y), a 2 equation system (in the video,A,y)); or 1 equation (see J.Fitness comment)
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Nice 🙂
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area of yellow square=34
27
34
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Answer is 34
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Please add Turkish subtitles
36
?=34
36 pure guess
Make sense 4x7 28. 6x7 42 so large so under 5
Dimensionless Quantities 🤔...I'll give ya this one....but let's step it up a bit and I think a really smart guy like you probably knows certain physical constants can't be normalized. ...I'm just digging a little deeper into math concepts and trying to be funny about it. Hope you are not offended in any way 🙂.
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Yellow area is 36 ( 29+43 =72. divided by 2 equal 36 ) yellow area MUST be 36. Cause WE do like 36 - 24 - 36…….LOL.
Per me ve la menate, c'è una soluzione molto più veloce