Question

The figure shows a semicircle on top of an isosceles right triangle. If the length of semicircle $\overline{AB}$ is $16\pi$, what is the approximate length of $\overline{BC}$?

• A. $2.8$
• B. $4.0$
• C. $5.7$
• D. $11.3$
• E. $22.6$

Answer 1

The correct option is E $22.6$

Let the length of $AB$ be $2r$ , where $r$ is radius of semicircle

Given that $\pi r=16\pi$

$\Rightarrow r=16$

The length of $BC$ is equal to $\frac{AB}{\sqrt{2}}=\frac{32}{\sqrt{2}}=22.6$

The correct option is $E$