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Problem 431

Geometry Difficulty 2.2 Find the answer CEMC Fermat · Canada · 2012

Five identical squares form rectangle $PQRS$ , as shown. The perimeter of rectangle $PQRS$ is 48. What is the area of $PQRS$ ?

Your answer

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

Official solution

Suppose that the side length of each of the five identical squares is $x$ .

Then $PS = QR = x$ and $PQ = SR = 5x$ .

Since the perimeter of rectangle $PQRS$ is 48, then $5x+x+5x+x=48$ or $12x=48$ or $x=4$ .

Therefore, $PS = QR = 4$ and $PQ = SR = 5 \cdot 4 = 20$ , and so the area of rectangle $PQRS$ is $20 \cdot 4 = 80$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.