Find the radius of a sector with a central angle of 30 degrees if its perimeter is the same value as its area.

Answer 1

The relevant formulas for arc length and sector area are easier if we use radians as the unit of angle measure. When we commit to that, we have the following: Arc length: s = rΘ ; Sector area: k = 1/2r²Θ

Θ = 30° = π/6

perimeter = 2r + r(π/6) = 1/2r²(π/6)

π/12r² - (2 + π/6)r = 0

r[π/12r - (2 + π/6)] = 0

π/12r = (2 + π/6) = (12 + π) / 12

r = (12 + π) / π