Question

The perimeter of a semicircle protractor is $108$ cm. Find the diameter of the protractor.

Answer 1

Let the radius of the semicircle $=rcm$

perimeter of the semicircle = $2r+\pi r$

semicircle = $2r+\pi r$

$=(2+\frac{22}{7})r$

$=\frac{14+22}{7}.r$

$=\frac{36}{7}.r\cdots \left(1\right)$

$p=108cm\cdots \left(2\right)$

$\left(1\right)=\left(2\right)$

$\frac{36}{7}r=108$

$r=\frac{108\times 7}{36}$

$r=3\times 7$

$r=21cm$

$\therefore$ Diameter of the semicircle $=2r$

$d=2\times 21cm$

$d=42cm$

$\therefore$ diameter $=42cm$