Question

A square fits exactly inside a circle with each vertices being on the circumference of the circle. The square has a side length of x cm. The areas of the circle is 56 cm squared. Work out the value of x.

Answer 1

Answer:

Therefore,

The value of x is 5.97 cm.

Step-by-step explanation:

Given:

Let the length of side of Square be "x" cm'.

Radius of Circle be "r"

Area of Circle = 56 cm squared

pi = 3.14

To Find:

x = ?

Solution:

We know Area of Circle is given by,

$\textrm{Area of Circle}=\pi r^{2}$

Substituting the values we get

$56=3.14\times r^{2}\\r^{2}=17.83\\Square\ Rooting\\r=\sqrt{17.83}=4.22\ cm$

We have, a square fits exactly inside a circle with each vertices being on the circumference of the circle,

Vertex Angle of a Square is 90°.

In a Circle Diameter Subtends a Right angle,

So it's Diagonal will be the Diameter,

$Diagonal =Diameter$

$Diameter=2\times Radius$

Substituting the values we get

$Diameter=2\times 4.22=8.44\ cm$

Therefore,

$Diagonal = 8.44\ cm$

Also we know that,

Length of Diagonal of a Square for side "x" is given by,

$Diagonal=\sqrt{2}\times x$

Substituting the values we get

$x=\dfrac{8.44}{\sqrt{2}}=5.967\approx 5.97\ cm$

Therefore,

The value of x is 5.97 cm.