What is the width of the sidewalk?

Question

A contractor is putting a cement sidewalk around a swimming pool. The pool is rectangular with a width of 20 feet and a length of 32 feet The sidewalk will have a length of x feet on each side. If the total area of the sidewalk and pool is 988 square feet.

Answer 1

Draw and label a diagram!!! Forget about the "x"!

w represents the width of the sidewalk

The total area of the pool and sidewalk is

(32 + 2w)(20 +2w) = 988

640 + 40w + 64w + 4w² = 988

4w² + 104w + 640 = 988

4w² + 104w - 348 = 0

w² + 26w - 87 = 0

(w - 3)(w + 29) = 0

 

Well the width of the sidewalk is 3 feet.