A geometry problem by Ajay Sambhriya

Geometry Level 2

The area of the square ABCD is 9 π 9\pi .
Find the perimeter of the circle inscribed inside this square.

Give your answer to 2 decimal places.


The answer is 16.70.

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2 solutions

We know that the area of a square is given by A = x 2 A=x^2 where x x is the side length. So

9 π = x 2 9\pi = x^2

x = 9 π = 3 π x=\sqrt{9\pi}=3\sqrt{\pi}

If a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square. The circumference of a circle is given by c = π d c=\pi d where d d is the diameter. So

c = π 3 π = 16.70 c=\pi * 3\sqrt{\pi}\approx = \boxed{16.70}

Ajay Sambhriya
Aug 25, 2016

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