Question

Sam and Charley have a rectangular swimming pool that is 8 feet wide and 14 feet long. They are going to build a tile border around the pool of uniform width. They have 75 square feet of tile. How wide is the border?

Answer 1

Answer:

The border is 1.5 feet wide

Step-by-step explanation:

The rectangular pool is 8 feet wide and 14 feet long.

Area of pool = (8 × 14) square feet

= 112 square feet.

The pool they are going to build is 75 square feet of tile. Let the width of this pool be x.

Then Length of pool + length of sidewalk = 14 + 2x

Width of pool + width of sidewalk = 8 + 2x

Then

(14 + 2x)(8 + 2x) - 112 = 75

112 + 28x + 16x + 4x² - 112 = 75

4x² + 44x - 75 = 0

Solving this using the quadratic formula

x = [-b ± √(b² - 4ac)]/2a

Where a = 4, b = 44, c = -75

x = [-44 ± √(44² - 4×4×(-75))]/2×4

= [-44 ± √(3236)]/8

= (-44 ± 56)/8

Ignoring the negative value for x

x = (-44 + 56)/8

= 12/8

= 1.5

The border is 1.5 feet wide