#### Answer

9 in

#### Work Step by Step

Given perimeter of the sector = 30 in.
The sector has arc length = 12 in
We need to find the length of the radius of the circle
It is the region bounded by two radii of the circle and arc intercepted by those radii
Perimeter of the sector = 2 *radius of the circle + arc length of sector
30 = 2 *radius of the circle + 12
30 - 12 = 2 *radius of the circle
18 = 2 *radius of the circle
radius of the circle = $\frac{18}{2}$ = 9 in