Question

ABСDIn the figure above, the radius of the inscribed circle is 10 inches (in.). What is the perimeter of square CABD?

Answer 1

Since the circle is inscribed in the square, we can conclude that the length of its diameter is equal to the length of one the sides of the square. Therefore:

$\begin{gathered} CA=2r \\ CA=2(10) \\ CA=20 \end{gathered}$

Since it is a square, all of its sides are equal, so:

$CA=AB=BD=DC$

The perimeter is the sum of all sides, and since all the sides are equal, then:

$\begin{gathered} P=4CA \\ P=4(20) \\ P=80in \end{gathered}$