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The figure shows a semicircle on top of an isosceles right triangle. If the length of semicircle $AB$ is $16 π units$ , what is the approximate length of $BC$ ?

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22.6 units

2 units

44 units

33 units

answer is A.

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Detailed Solution

Given,

Perimeter of a semicircle is

πr

.
Let the length of

AB

2 r

, where

r

is the radius of a semicircle.

\Rightarrow

πr = 16 π

\Rightarrow r = 16

units
The length of

BC

is equal to

\frac{AB}{\sqrt{2}}

since the triangle is a right angled isosceles triangle.

\Rightarrow

The length of

BC = \frac{32}{\sqrt{2}}

\Rightarrow

The length of

BC = 22.6

units.
So, the correct option is

1

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