, 2012

Let $PQ=a$, $QR=b$, $PW=c$, and $WV=d$. Since the large rectangle is divided into four smaller rectangles, then $PQ=WX=VU=a$, $QR=XS=UT=b$, $PW=QX=RS=c$, and $WV=XU=ST=d$. Since the area of rectangle $PQXW$ is 9, then $ac=9$. Since the area of rectangle $QRSX$ is 10, then $bc=10$. Since the area of rectangle $XSTU$ is 15, then $bd=15$. The area of rectangle $WXUV$ is $ad$. We want to determine the value of $ad$. If we multiply the equations $ac=9$ and $bd=15$, we obtain $(ac)(bd)=9\times 15$, or $abcd=135$. We divided this equation by the equation $bc=10$. This gives $\dfrac{abcd}{bc} = \dfrac{135}{10} = \dfrac{27}{2}$, from which $ad=\dfrac{27}{2}$.