Quadratic Word Problem

Question

You want to build a fence around a rectangular yard. The width is 1/2 the length and the area is 338 square feet. How many feet of fencing will you need?

Answer 1

Area = 338 square feet

Width (y) = 1/2 the length = 1/2*x, where x is the length of the fencing.

The area of the rectangle is A = xy.

(x/2)(x) = 338 ⇒ x²/2 = 338

Solve for x.

x² = 676 ⇒ x = ± 26 (negative solution doesn't exist)

We need 26 feet of fencing for the rectangular yard.