In the diagram, rectangle $P R T V$ is divided into four rectangles. The area of rectangle $P Q X W$ is 9 . The area of rectangle $Q R S X$ is 10 . The area of rectangle $X S T U$ is 15 . What is the area of rectangle $W X U V$ ?
(A) 6
(B) $\frac{27}{2}$
(C) 14
(D) $\frac{50}{3}$
(E) $\frac{95}{2}$

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-070.jpg?height=360&width=377&top_left_y=1457&top_left_x=1297)
Let $P Q=a, Q R=b, P W=c$, and $W V=d$.

Since the large rectangle is divided into four smaller rectangles, then $P Q=W X=V U=a$, $Q R=X S=U T=b, P W=Q X=R S=c$, and $W V=X U=S T=d$.

Since the area of rectangle $P Q X W$ is 9 , then $a c=9$.

Since the area of rectangle $Q R S X$ is 10 , then $b c=10$.

Since the area of rectangle $X S T U$ is 15 , then $b d=15$.

The area of rectangle $W X U V$ is $a d$. We want to determine the value of $a d$.

If we multiply the equations $a c=9$ and $b d=15$, we obtain $(a c)(b d)=9 \times 15$, or $a b c d=135$.

We divided this equation by the equation $b c=10$.

This gives $\frac{a b c d}{b c}=\frac{135}{10}=\frac{27}{2}$, from which $a d=\frac{27}{2}$.

ANSWER: (B)