CEMC Cayley

Geometry Difficulty 2.5 Junior Find the answer

Four congruent rectangles and a square are assembled without overlapping to form a large square. Each of the rectangles has a perimeter of 40 cm. What is the total area of the large square?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Suppose that each of the smaller rectangles has a longer side of length $x \mathrm{~cm}$ and a shorter side of length $y \mathrm{~cm}$ . Since the perimeter of each of the rectangles is 40 cm, then $2x+2y=40$ or $x+y=20$ . But the side length of the large square is $x+y \mathrm{~cm}$ . Therefore, the area of the large square is $(x+y)^{2}=20^{2}=400 \mathrm{~cm}^{2}$ .

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