A man built a walk of uniform width around a rectangular poo

A man built a walk of uniform width around a rectangular pool, if the area the walk is 225 square feet and the dimensions of the pool are If feat by 6 feet, how wide is the walk

Solution

Given Area of side walk = 225 ft²

length = (10 + 2w) , width = (6 + 2w)

==> (10 + 2w)(6 + 2w) - (Area of pool) = 225

==> (60 + 20w + 12w + 4w²) - (10 * 6) = 225

==> 60 + 32w + 4w² - 60 = 225

==> 32w + 4w² = 225

==> 4(w² + 8w) = 225

==> 4(w² + 2w(4) + 4² - 4²) = 225

==> 4((w + 4)² - 16) = 225

==> (w + 4)² - 16 = 225/4

==> (w + 4)² = 225/4 +16

==> (w + 4)² = 289/4

==> w +4 = 17/2 , -17/2

==> w = 17/2 -4 , -17/2 -4

==> w = 9/2 , -25/2

as measure of width cannot be negative

==> w = 9/2 = 4.5 ft