Final answer:
The length of the shorter side of the rectangle is 17 feet.
Step-by-step explanation:
Let's assume that the shorter side of the rectangle is represented by x feet. According to the problem, the longer side is 11 feet shorter than five times the shorter side, so it can be represented as 5x - 11 feet.
The formula for the perimeter of a rectangle is 2(length + width). Since the length is 5x - 11 feet and the width is x feet, we can write the equation:
2((5x -11) + x) = 182
Simplifying the equation, we get:
12x - 22 = 182
12x = 204
x = 17
Therefore, the length of the shorter side is 17 feet, which corresponds to option A.