13. The diagram shows a quadrilateral $P Q R S$ made from two similar right-angled triangles, $P Q R$ and $P R S$. The length of $P Q$ is 3 , the length of $Q R$ is 4 and $\angle P R Q=\angle P S R$.
What is the perimeter of $P Q R S$ ?
A 22
B $22 \frac{5}{6}$
C 27
D 32
E $\quad 45 \frac{1}{3}$
13. A Pythagoras' Theorem shows that $P R=\sqrt{3^{2}+4^{2}}=5$. So the perimeter of triangle $P Q R$ is 12. Since the triangles are similar and $P R: P Q=5: 3$ we see that the perimeter of triangle $P R S$ is 20 . Hence the perimeter of $P Q R S$ is $12+20-2 \times P R=32-10=22$.