A rectangle is divided into four smaller rectangles, labelled W, X, Y, and Z, as shown. The perimeters of rectangles $\mathrm{W}, \mathrm{X}$ and $\mathrm{Y}$ are 2, 3 and 5 , respectively. What is the perimeter of rectangle $\mathrm{Z}$ ?
(A) 6
(B) 7
(C) 4
(D) 8
(E) 7.5

| $W$ | $X$ |
| :---: | :---: |
| $Y$ | $Z$ |
Label the lengths of the vertical and horizontal segments as $a, b, c, d$, as shown.

| $c$ | $d$ |
| :---: | :---: |
| $\mathrm{W}$ | $\mathrm{X}$ |
| $\mathrm{W}$ | $\mathrm{Y}$ |
| $\mathrm{Y}$ | $\mathrm{Z}$ |

Rectangle $\mathrm{W}$ is $b$ by $c$, so its perimeter is $2 b+2 c$, which equals 2 .

Rectangle $\mathrm{X}$ is $b$ by $d$, so its perimeter is $2 b+2 d$, which equals 3 .

Rectangle $\mathrm{Y}$ is $a$ by $c$, so its perimeter is $2 a+2 c$, which equals 5 .

Rectangle $\mathrm{Z}$ is $a$ by $d$, so its perimeter is $2 a+2 d$.

Therefore, $2 a+2 d=(2 a+2 b+2 c+2 d)-(2 b+2 c)=(2 a+2 c)+(2 b+2 d)-(2 b+2 c)=5+3-2=6$.

ANSWER: (A)