Question

A gardener has a circular flower bed with a radius of 17 feet. If she wants to make a square flower bed with the same area as the circular one, what will the length of each side be to the nearest thousandth?

Answer 1

We know that

• The radius is 17 feet.

First, we find the circular area

$\begin{gathered} A=\pi(r)^2 \\ A=3.14(14)^2\approx3.14\cdot196\approx615.44ft^2 \end{gathered}$

This means the square flower bed will have an area of 615.44 square feet. So, we find its sides with the formula for squared areas

$\begin{gathered} A=l^2 \\ 615.44=l^2 \\ l=\sqrt{615.44}\approx24.808 \end{gathered}$

Therefore, the bed should have sides of 24.808 feet, approximately.