How could I find all the possible radii of a sector a cirle with a perimeter of 12 cm and area of 8 cm^2?

Answer 1

Perimeter=2r+r*theta
area=r^2*theta

set the top equation to 12, and the bottome to 8

12=2r+r*theta
8=r^2*theta

from the lower, theta=8/r^2, put that in the top,
12=2r+8/r
multipy both sides by r, then use the quadratic equation to solve for r.

Answer 2

2 cm or 4 cm