Answer:
The border is 1.5 feet wide
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