Question

If Figure 4, the perimeter of isosceles trapezoid $ABCD$ is $50$. If $BC=9$ and $AD=21$, calculate the length of diagonal $\overline{AC}$.

• A. 13
• B. 14
• C. 15
• D. 16
• E. 17

Answer 1

The correct option is E 17

Given, $BC=9,AD=21$

$\Rightarrow AB=CD=\frac{(50-21-9)}{2}=10$
Let $h$ be the length of perpendicular drawn from $B$ to $AD$.

We get $h=\sqrt{{10}^2-6^2}=\sqrt{64}=8$
$\Rightarrow AC=\sqrt{{15}^2+8^2}=\sqrt{289}=17$