Question

A square fits exactly inside a circle with each of its vertices being on the circumference of the circle.

Answer 1

Answer:

The side of the square is 5.971 cm

Step-by-step explanation:

If the square fits the circle exactly, then its diagonal is equal to the diameter of the circle. Since the side of the square has a length of $x$ cm, then it's diagonal have the length of $x\sqrt2$ cm. Using the circle's area we can find the diagonal of the square, as shown below:

$area = \pi*r^2\\56 = pi*r^2\\r^2 = \frac{56}{\pi}\\r = \sqrt{\frac{56}{\pi}}\\r = 4.222$

Since the diameter of the circle is the same as the diagonal of the square, then:

$x\sqrt{2} = 2*r \\x = \frac{2*r}{\sqrt{2}}\\x = \frac{2*4.222}{\sqrt{2}}\\x = 5.971$

The side of the square is 5.971 cm

Answer 2

Answer:

5.97

Step-by-step explanation: