Answer
The radius of the largest circular region is $5.6\;ft$.
Work Step by Step
Let the radius of the circle be $=r$.
Area of the circle $=\pi r^2$.
Given area of the circle $=100\;ft^2$.
Equate both areas.
$\Rightarrow \pi r^2=100$
Divide both sides by $\pi$.
$\Rightarrow \frac{\pi r^2}{\pi}=\frac{100}{\pi}$
Simplify.
$\Rightarrow r^2=\frac{100}{\pi}$
Take the square root on both sides.
$\Rightarrow \sqrt{ r^2}=\pm\sqrt{\frac{100}{\pi}}$
Simplify.
$\Rightarrow r=\pm5.6\;$
The area cannot have a negative sign.
Hence, the radius of the circle is $5.6\;ft$.
