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UKMT Intermediate Mathematical Challenge, 2017

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The diagram shows a quadrilateral $PQRS$ made from two similar right-angled triangles, $PQR$ and $PRS$ . The length of $PQ$ is $3$ , the length of $QR$ is $4$ and $\angle PRQ = \angle PSR$ . What is the perimeter of $PQRS$ ?

(A) $22$ (B) $22\frac{5}{6}$ (C) $27$ (D) $32$ (E) $45\frac{1}{3}$

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