#### Answer

The smallest possible value of the perimeter is 24 inches.

#### Work Step by Step

For a given area, the rectangle with the smallest perimeter is a square. If the area is $36~in^2$, then each side of the square has a length of $6~in$
We can find the perimeter:
$P = (4)(6~in) = 24~in$
The smallest possible value of the perimeter is 24 inches.