Question

A square fits exactly inside a circle with each of its vertices

being on the circumference of the circle.
The square has sides of length xcm.
The area of the circle is 56 cm?.
Work out the value of x.
Give your answer correct to 3 significant figures.​

Answer 1

5.97

Explanation:

If the radius of the circle = r then

pi r^2 = 56

r^2 = 56/pi

r = sqrt(56/pi)

The radius of the circle is equal to half of a diagonal of the square. That is,

r = (1/2) sqrt (2x^2)

= x (sqrt 2)/2

= x/(sqrt 2)

So x = r sqrt 2

= sqrt (56/pi) sqrt 2

= 4 sqrt (7/pi)

= 5.9708