In the figure shown, $P Q R S$ has three sides of equal length and $S R=16 \mathrm{~cm}$. If the perimeter of $P Q R S$ is $40 \mathrm{~cm}$, then the length of $P Q$ is
(A) $6 \mathrm{~cm}$
(B) $7 \mathrm{~cm}$
(C) $8 \mathrm{~cm}$
(D) $9 \mathrm{~cm}$
(E) $10 \mathrm{~cm}$

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-002.jpg?height=181&width=412&top_left_y=1598&top_left_x=1277)
Since the perimeter of $P Q R S$ is $40 \mathrm{~cm}$ and $S R=16 \mathrm{~cm}$, then the combined length of the remaining three sides is $40 \mathrm{~cm}-16 \mathrm{~cm}=24 \mathrm{~cm}$.

Each of the remaining three sides is equal in length, and so $P Q=\frac{24 \mathrm{~cm}}{3}=8 \mathrm{~cm}$.

ANSWER: $(\mathrm{C})$