Algebra- inground pool

Question

A couple have designed a new in-ground swimming pool for their backyard. The pool is rectangular and measures 4040 feet by 3030 feet. They have also designed a tile border to go around the pool. In the diagram to the right, this border is x feet wide. The tile border covers 296296 square feet in area. What is the width x of this tile border? (Hint: Find an expression for the area of the large rectangle and subtract an expression for the area of the small rectangle.)

Answer 1

Pool is 40(30) = 1200 ft²

 

Pool and border is (x + 40)(x + 30) = x² + 70x + 1200 ft²

 

x² + 70x + 1200 - 296 = 1200

x² + 70x - 296 = 0

(x + 74)(x - 4) = 0

 

x + 74 = 0

x = -74

Since we don't measure in negative numbers, we disregard this solution.

 

x - 4 = 0

x = 4