What is the area of the square? The 5 rectangles puzzle

Thanks to Surjadi from Indonesia for the suggestion!

Twitter Cshearer41
solution by @birkhofyan

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[JeffAtkins]

uggh... embarrassed that I gave up too soon on such an easy solution... going to blame this one on me being tired... thanks for the video.

[davidseed]

Neat, but how about a solution that is pure geometry. The three rectangles below the orange rectangle can be replaced by three orange rectangles since they have the same width and area. So the left hand side of the square is 4 orange rectangles of height 4 so total edgelength=16 hence area=256

[logantotesrocks]

His solution is a lot easier than what I did😂

[gamingmusicandjokesandabit]

The individual rectangles inside the square, whose area you didn't measure: Am I a joke to you?

[retryxfff]

My solution is:
Let X be the length of one side of square.
The area of each rectangle is X^2/5,
which means the length of smaller side of blue rectangle is X/5, and the other side of orange rectangle is 4X/5.
Now we have an equation: 4X/5 × 4 = X^2/5, and X = 16.

[LightningStrm]

Oh wow, I was making this way harder than it needed to be.

[everydayjokes]

Joke of the day:
What is the soft stuff between sharks teeth?
*slow swimmers.*

[tushroy]

The first "Mind Your Decision" problem that I could solve. I am very happy. Continue your work Presh. I am a great fan of you dude.

[pedronunes]

I did it in another way:




The blue rectangle must have sides L and L/5. So the longer side of the orange square has lenght 4L/5. So the shorter one must have lenght L/4. So L/4 = 4 L=16 Area = 256

[MrAqr]

Wow, that was simple. I went so far as to set 5 variables and solve each one and find the area afterwards...

[pasteltiara]

Fantastic.... Love this subscription. So elegantly simple.

[t]

Good, surprisingly simple solution. My first instinct as an engineer was to create a big system of linear equations. My second instinct was to find a way to cut each rectangle into triangles that can tile another rectangle. My third instinct was to not spend an hour on a two-minute problem and just watch the solution. That was the right choice.

[michaelgeiss]

Elegant! Replace the yellow green and pink rectangles with three orange rectangles. (4*4)^2=256.

[hisanimations]

It's amazing how we think that it would be a complicated answer when it is so simple!

[yourmathtutorvids]

Thanks for taking my mind off the Sunday scaries for a bit!

[muhammadmuqsith]

You can also directly do with the blue rectangle because it already spans the entire side of the square. Suppose its length is x. The width will be x/5. Therefore the length of the orange one is 4x/5. Then, 4*4x/5 equals x*x/5. There you have it, x=16

[SphereManDan]

This is drawn to scale as well. Almost to the exact pixel. you can just measure what u labeled side b and get a ratio from 4. Side 4 was 218 pixels high. Side b was 562 pixels high. or almost exactly 3 of side labeled 4. So 3*4=12. Getting the same solution.

[Jop_pop]

Let the side length of the square be x. Yellow triangle has sides x-4 and y. Green and Pink are congruent since they share a side and have the same area. So their vertical sides are half that of yellow. So cut yellow in half to fit it into green. This shows that the long side of orange is 3y. So orange = yellow gives (x-4)y=4(3y) which simplifies to xy=16y so x=16. x^2 = 256

[jasonxng]

Such an elegant solution! The comment section’s method was so much slower lol

[MaxMathGames]

One of the simplest questions on your channel
But as usual, awesome presentation work 👍👍👍❤️❤️❤️