# The perimeter of a semicircle is 25.7 kilometers. What is the semicircle's diameter?

Feb 18, 2018

Diameter of the semicircle = 10 km.

#### Explanation:

perimeter of semicircle = $\frac{1}{2}$ the circumference + diameter

Given: perimeter of semicircle =$25.7 k m$

Circumference of circle with radius $r$= $2 \pi r$ where $2 r$= diameter

$\implies 25.7 = \frac{1}{2} \times 2 \pi r + 2 r$

$\implies 25.7 = \pi r + 2 r = r \left(\pi + 2\right)$

$\implies 25.7 = r \left(3.14 + 2\right) = r \left(5.14\right)$

$\implies r = \frac{25.7}{5.14} = 5$

$\therefore r a \mathrm{di} u s = 5 k m$

$\implies \mathrm{di} a m e t e r = 2 r = 10 k m$