The square above is composed of five rectangles, which are equal in area.
You are given the length of one side to be equal to 3 units.
Determine the area of the square.
Solution to the Problem:
The area of the square is 144 square units.
Click here for Davit Banana's solution
Colin Bowey had a different way of solving the problem:
Let the side length of the square be S.
The orange rectangle has height 3, so the combined height of the green and pink rectangles is:
S - 3
Since the green and pink rectangles have equal areas and the same width, their heights are equal, so each has height:
(S - 3) / 2
It turns out the rectangles were all equal after all; they were just expressing themselves differently.
Now compare the yellow rectangle with either the green or pink rectangle. The yellow rectangle has height S - 3, which is twice the height of the green or pink rectangle.
Because all five rectangles have equal area, the yellow rectangle must therefore have half their width.
If the width of the yellow rectangle is x, then the width of the green and pink rectangles is 2x.
Once the 2:1 relationship appeared, the rectangles more or less boxed themselves into the answer.
The orange rectangle spans both of these widths, so its width is:
x + 2x = 3x
Its area is therefore:
3 × 3x = 9x
The yellow rectangle has the same area:
x(S - 3) = 9x
Cancelling x:
S - 3 = 9
Therefore:
S = 12
In the end, the square had nowhere left to hide — its side length had to be 12.
So, after a little rectangular wrangling, the area of the square is:
12^2 = 144 square units