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Beautiful Geometry 1

Five Rectangles in a Square

A square is split into five rectangles with equal areas. What’s the area of the square?

We have that

S_{PURPLE} + S_{GREEN} + S_{BLUE} = 3S_{ORANGE}.

Therefore, the length of the purple rectangle is 2 \times 3 = 6 and the side of the square is 6 + 2 = 8. Thus, the area of the square is 8 \times 8 = 64.

Puzzle Newsletter (Post) (#10)
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