In the diagram, the area of square $Q R S T$ is 36 . Also, the length of $P Q$ is one-half of the length of $Q R$. What is the perimeter of rectangle $P R S U$ ?
(A) 24
(B) 30
(C) 90
(D) 45
(E) 48

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-045.jpg?height=315&width=401&top_left_y=1813&top_left_x=1315)
Since square $Q R S T$ has area 36, then its side length is $\sqrt{36}=6$.

Therefore, $Q R=6$ and $R S=6$.

Since $P Q=\frac{1}{2} Q R$, then $P Q=3$.

Now rectangle $P R S U$ has height $R S=6$ and width $P R=P Q+Q R=3+6=9$.

Therefore, the perimeter of $P R S U$ is $2(6)+2(9)=12+18=30$.

ANswer: (B)