Question

A circular pool is enclosed by a square fence so that the pool touches the fence in four places, as shown in the figure below. If the circumference of the pool is 100π feet, how much fencing was used to enclose the area?

Answer 1

Note that the each side of the square fence is the same length as the diameter of the circular pool (you can see this by drawing the line joining the midpoints of opposite sides of the square)

Recall that the circumference of a circle of radius r is \(2\pi r\).
Equate this with the given circumference to get the radius and then the diameter which gives each side of the square.
Now calculate the perimeter of the square to get the final answer .
(perimeter of a square = 4 * length of each side)