Question

A square fits exactly inside of a circle with each of it's vertices being on the circumference of the circle. The square has sides of length x cm. The area of the circle is 56cm^2. Work out x

Answer 1

`5.971\ cm`

Explanation:

The computation of x is given below:

As we know that

`Area = \pi r^2\\\\56 = \pi r^2\\\\r^2 = (56)/(\pi) \\\\r = \sqrt{(56)/(\pi) }`

= 4.22

Now the diameter of the square would be similar to the diameter of the circle

So,

`x√(2) = 2* r \\\\x = (2* r)/(√(2) ) \\\\= (2* 4.22)/(√(2) ) \\\\= 5.971\ cm`