An in ground rectangular pool has a concrete pathway surrounding the pool. if the pool is 16 feet by 32 feet and the entire area

Question

lys-0071 [83]

2 years ago

15

An in ground rectangular pool has a concrete pathway surrounding the pool. if the pool is 16 feet by 32 feet and the entire area

of the pool including the walkaway is 924 ft^2, find the width of the walkway

Mathematics

1 answer:

Anastasy [175] · Answer 1 · 2023-05-06T05:36:03+03:00

1. Let's call:

x: the width of the walkway.
b: 2x+16 (there is a widht "x" of the walkway on each side).
h: 2x+32 (there is a widht "x" of the walkway on each side).
A: 924 ft^2 ( the area of the pool of including the walkway).

2. The area of a rectangle is:

A=(b)(h)

b: the base of the rectangle (2x+16)
a: the height of the rectangle (2x+32)

3. Then, we have a quadratic equation:

924=(2x+16)(2x+32)
4x^2+64x+32x+512-924=0
4x^2+96x-412=0

4. We apply the quadratic formula to find the value of "x":

x=(-b±√(b^2-4ac))/2a

x=3.71

The answer is: The width of the walkway is 3.71 ft