Question

A dog trainer has 104 ft of fencing that will be used to create a rectangular work area for dogs. If the trainer wants to enclose an area of 576 ft square, what will the dimensions of the work area?

Answer 1

36 ft by 16 ft

Explanation:

To solve this problem, you need to find dimensions of a rectangle such that the perimeter is 104 ft and the area is 576 ft. The perimeter is twice the sum of length and width, so the sum of length and width is 52 ft.

The area is the product of length and width, so if w represents the width, we have ...

w(52 -w) = 576

w² -52w = -576 . . . . . eliminate parentheses, multiply by -1

w² -52w +26² = 26² -576 . . . . . . complete the square

(w -26)² = 676 -576 = 100

w = 26 ±√100 = {16, 36}

If the width is the short dimension, it is 16 feet. Then the length is 36 feet.