MATH SOLVE

2 months ago

Q:
# . An inground 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 walkway is 924 ft2, find the width of the walkway.

Accepted Solution

A:

For this case we have that the pool area without including the walkway isA = (16) * (32) = 512ft ^ 2

Then, we have that the entire area of the pool including the walkway is

Aw = 924 ft2.

(16 + 2w) * (32 + 2w) = 924

512 + 32w + 64w + 4w ^ 2 = 924

512 + 96w + 4w ^ 2 = 924

Solving for w> 0

-412 + 96w + 4w ^ 2 = 0

w = 3.72 ft

answer

the width of the walkway is w = 3.72 ft

Then, we have that the entire area of the pool including the walkway is

Aw = 924 ft2.

(16 + 2w) * (32 + 2w) = 924

512 + 32w + 64w + 4w ^ 2 = 924

512 + 96w + 4w ^ 2 = 924

Solving for w> 0

-412 + 96w + 4w ^ 2 = 0

w = 3.72 ft

answer

the width of the walkway is w = 3.72 ft