Multicolor Square Problem

For more geometry challenges, check out the above link! Let me know what you think!

[tannerhills]

My favorite videos to watch on YouTube and it feels weird but “how exciting” it is to find the solution to these problems.

[bogdan.shahnitsky]

There's an even simpler solution:
1) There are Yellow, Green and Pink rectangles under the Orange one. That means, that the combined rectangle YGP (containing the Yellow, Green and Pink rectangles) have the same width as the Orange one.
2) The area of the YGP rectangle is 3 times greater than the area of the Orange rectangle (since it's a composite of 3 rectangles of same area)
3) Since Orange and YGP have the same width and the are ratio of 1/3, that means that their height ratio is also 1/3, resulting in the YGP height is 9
4) The side of the Square is 3 + 9 = 12, and the area is 144

[facesmile]

No bs, no weird promotions, no trying to act important, and so on.
Just plain old crystal clear problem solving.
This is oddly satisfying hahaha!

[LIOTBs]

These are awesome! Keep them coming. It has also been a really good refresher course.

[kruup]

This problem have different ways to solve it, how exiting!

[-blank-]

i did it an easier way. The yellow, green, and pink rectangles make a big rectangle with unknown lengths. Lets call those lengths x and y. The area of that rectangle is then xy. Area of orange rectangle = 3x. we know that the area of the orange rectange is 1/3 times the area of the combined rectangle. therefore 3(3x) = xy. 9x = xy. y = 9. Therefore the length of one side of the square is 3 + 9 = 12. 12 * 12 = 144.

[dezzi]

andy thank you for smiling as you make these videos; truly wonderful and interesting to watch!

[jirkakalecky]

My solution was Yellow+Green+Pink = 3x Orange, so I must be able to place 3 other Oranges bellow the one given, so I am left with 4x orange and a blue. each orange has the side of 3, so 4x3 = 12 = x ...

[mekaindo]

I love how you only needed to analize 2 squares out of 5 to get the answer

[JasonLuther]

I really appreciate these videos. Helps keep out problem solving skills sharp, applicable to many real world applications

[vandal_]

The exact problem was in my maths competition for 8th graders that was in february this year, love to see your solution.

[laxed]

Simpler Solution:
Area of orange box = 3x, where x is the unknown side of the orange box
Area of all boxes but the blue = x * the side length of the whole square
So the side length of the whole square = the area of all but blue divided by the top side of the orange box, x: 12x / x = 12
Square this to get the area of the whole square: 12^2 = 144

[lux]

"Let's put a box around it." i love you andy

[pault]

I like your videos - straight forward, not wasting time rewriting equations ad infinitum to add minutes.
I also solved this the simpler way it's been discussed in comments, but also have a small problem with the presentation. Put simply, we had to assume the smaller portions were all rectangles, even though it wasn't stated.

[Gabush]

i love these videos, they keep me in practice during the holidays!!!

[jonsebastian]

Another solution
Green and pink are equal, because areas and horizontal sides also are. So as yellow vertical is 2*(green or pink) vertical, and the areas are the same, yellow horizontal its ½ green vertical

[crazylegskc]

I always seem to solve the problem in a more complicated way than you! The blue rectangle was the only one that I didn't use while solving it, and I ended up taking a lot more steps than you. But I still got the right answer. How exciting!

[dansheppard]

Another algebra-free way.
1. Green and pink are the same width so, because they're the same area, they're also the same height as each other, ie they're identical.
2. Yellow is twice as high as either green or pink so is half as wide as them.
3. Orange is three times the width of yellow because it's as wide as yellow and green, and green is twice as wide as yellow.
4. If orange is three times as wide as yellow, it's a third of the height, so yellow has height 9, and the square height 12.
5. You can use the fact we know that it's square to get the answer, 144.

[oboealto]

A whole world would have been way better at math (and consequently a lot of other fields that use math, namely, almost everything) if you were their math teacher.

[shawnmcgrath]

I solved it a different, and I think easier way: Ignore the blue rectangle. If you re-shape the orange, green and pink rectangles so they're the same shape as the orange one while preserving their area, all four will be exactly the same as the orange one... therefore there's 4 that can fit into the whole square minus the blue rectangle, therefore the side length is 4 x 3 = 12