Question

In Figure 4, the perimeter of isosceles trapezoid $WXYZ$ is $62$. If $\overline{ZY}=7$ and $\overline{WX}=25$, calculate the length of diagonal $WY$.

• A. $15$
• B. $17$
• C. $20$
• D. $25$
• E. $26$

Answer 1

The correct option is C $20$

$WZ=XY=\frac{(62-25-7)}{2}=15$
Let the $h$ be the length of perpendicular drawn from $Y$ to $XW$, we get

$h=\sqrt{{15}^2-9^2}=\sqrt{144}=12$
$\Rightarrow WZ=\sqrt{{16}^2+{12}^2}=\sqrt{400}=20$