13. A rectangular strip of paper of dimensions $4 \times 13$ is folded as shown in the diagram. Two rectangles are formed with areas $P$ and $Q$ where $P=2 Q$. What is the value of $x$ ?
A 5
B 5.5
C 6
D 6.5
E $4 \sqrt{2}$
SolUTION
C

Let the height of the rectangle $Q$ be $y$. Since the original $4 \times 13$ rectangle has been folded to form the second shape, both the width of the rectangle with area $Q$ and the height of the rectangle with area $P$ are 4. Considering the base of the rectangle before and after folding gives the equation $x+4+y=13$ and hence $x+y=9$. Since the two rectangles both have one side of length 4 , the condition $P=2 Q$ implies that $x=2 y$ and so $y=3$ and $x=6$.