Question

A sector of a circle of radius "r" cm has an area of "A"cm². Express the perimeter of the sector in terms of "r" and "A"

Answer 1

Answer:

2A/r + 2r

Step-by-step explanation:

A sector is made of an arc and two radii. As such, the perimeter of the sector is the sum of the length of an arc and the two radii. Given that the radius is r and the area is A, the area of a sector A

= Ф°/360° * πr²

The length L of an arc of the sector

= Ф°/360° * 2πr

Hence,

A/L = r/2

L = 2A/r

The perimeter of the sector

= L + 2r

= 2A/r + 2r