Question

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

Answer 1

9.94 miles.

Explanation:

We know the perimeter of semi circle = `pi r + 2r` unit. [ where r is the radius of semi circle.]

Hence `pi r + 2r = 25.7`miles

`rArr r(pi + 2) = 25.7`

`rArr r (22/7 + 2) = 25.7`

`rArr r = 25.7 * 7/36 = 4.97` miles.

So, Diameter = 2r = 2 * 4.97 = 9.94 miles

Answer 2

Exact r is 4.9985 miles and diameter is approximately 10 miles

Explanation:

The previous solution way is correct but I used exact values (for pi).

`pi*r + 2*r = 25.7` miles

pi is 3.141592654

Therefore,

`5.141592654*r = 25.7` miles

`r=25.7/5.141592654`

`r=4.9985` miles.

Diameter is `=2*r=9.9969` miles. Diameter is approximately 10 miles.