A rectangular swimming pool that is 10 ft wide by 16 ft long is surrounded by a cement sidewalk of uniform width. If the area of

Question

just olya [345]

2 years ago

15

A rectangular swimming pool that is 10 ft wide by 16 ft long is surrounded by a cement sidewalk of uniform width. If the area of

the sidewalk is 155 ft2, what is its width?

Mathematics

1 answer:

Alchen [17] · Answer 1 · 2022-06-03T20:46:03+03:00

We are asked to solve for the width "x" in the given problem. To visualize the problem, see attached drawing.
We have the area of the swimming pool such as:
Area SP = l x w
Area SP = 10 * 16
Area SP = 160 feet2
Area of the swimming pool plus the sidewalk with uniform width:
Area SP + SW = (10 + x) * (16 + x)
160 + 155 = 160 + 10x + 16x + x2
160 -160 + 155 = 26x + x2
155 = 26 x + x2
x2 + 26x -155= 0
Solving for x, we need to use quadratic formula and the answer is 5 feet.

The value of x is <span>5 feet. </span>