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Problem 350

Geometry Difficulty 2.4 Multiple choice CEMC Pascal · Canada · 2016

In the diagram, the area of square $QRST$ is 36. Also, the length of $PQ$ is one-half of the length of $QR$ .

What is the perimeter of rectangle $PRSU$ ?

Pick one

Official solution

Since square $QRST$ has area 36, then its side length is $\sqrt{36}=6$ .

Therefore, $QR = 6$ and $RS=6$ .

Since $PQ = \frac{1}{2}QR$ , then $PQ = 3$ .

Now rectangle $PRSU$ has height $RS = 6$ and width $PR = PQ + QR = 3+6=9$ .

Therefore, the perimeter of $PRSU$ is $2(6) + 2(9) = 12+18=30$ .

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