Question

The circumference of the semicircle is 108 cm. if the side of a square is 30% more the diameter of the semicircle, what is the perimeter of the square ?

Answer 1

circumference = rtheta or 2"pi"r
diameter = 2r 
therefore , 108 = 2 pi r  , 2r = 108/pi
side of sq is 30% more than the diameter 
= 108/pi + 30/100*108/pi
=44.69

Answer 2

Answer-

Perimeter of square is 218.68 sq.units

Solution-

We know, circumference of a semicircle with radius r is,

$c=\pi r+2r$

Given, the circumference of the semicircle = 108 cm

So,

$\Rightarrow \pi r+2r=108$

$\Rightarrow r(\pi +2)=108$

$\Rightarrow r= \frac{108}{\pi +2}$

$\Rightarrow r=21.01$

Then diameter of the semi-circle d is 2×21.01=42.02 cm

The side of the square is 30% more the diameter of the semicircle, so length of the side is,

$=d+\frac{30d}{100}\\\\= 42.02+\frac{30\times 42.02}{100}\\\\=54.67$

Perimeter of square is,

$4\times 54.67=218.68$