Perimeter Ratio, Squares

Given a circle of radius x, a square inscribed in the circle, and another square circumscribed about the circle, what is the ratio of the perimeter of the outer square to that of the inner square?

Show/Hide Solution

If we draw the inner square in a foxy way, we get what we need.

As shown in the diagram, the outer perimeter is 8x.

The inner perimeter is 4(x2) = 4x2.

The ratio is  8x  =  2  =  2
4x2 2 1

Leave a Reply

Your email address will not be published. Required fields are marked *