Solve the problem. Round answer to the nearest hundredth. Please Show All Work!
Suppose a pool has dimensions 12 ft. by 30 ft. A sidewalk of uniform width around the pool has an area of 200 square feet. What is the width of the walkway?
Let w be the sidewalk width.
The total sidewalk area will be
24w + 60w + 4w^2.
Drawing yourself a figure should show you why. The 4w^2 term is the area of the corners.
Set that equal to 200 and solve for w.
4w^2 +84w - 200 = 0
w^2 + 21w -50 = 0
You need to use the quadratic equation on that. It does not factor easily, an the roots are no integers.
w = [-21 + sqrt641]/2 = 2.159 feet is the positive root. Ignore the negative solution.