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}](https://tex.z-dn.net/?f=%5Ctextrm%7BArea%20of%20Circle%7D%3D%5Cpi%20r%5E%7B2%7D)
Substituting the values we get
![56=3.14\times r^{2}\\r^{2}=17.83\\Square\ Rooting\\r=\sqrt{17.83}=4.22\ cm](https://tex.z-dn.net/?f=56%3D3.14%5Ctimes%20r%5E%7B2%7D%5C%5Cr%5E%7B2%7D%3D17.83%5C%5CSquare%5C%20Rooting%5C%5Cr%3D%5Csqrt%7B17.83%7D%3D4.22%5C%20cm)
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](https://tex.z-dn.net/?f=Diagonal%20%3DDiameter)
![Diameter=2\times Radius](https://tex.z-dn.net/?f=Diameter%3D2%5Ctimes%20Radius)
Substituting the values we get
![Diameter=2\times 4.22=8.44\ cm](https://tex.z-dn.net/?f=Diameter%3D2%5Ctimes%204.22%3D8.44%5C%20cm)
Therefore,
![Diagonal = 8.44\ cm](https://tex.z-dn.net/?f=Diagonal%20%3D%208.44%5C%20cm)
Also we know that,
Length of Diagonal of a Square for side "x" is given by,
![Diagonal=\sqrt{2}\times x](https://tex.z-dn.net/?f=Diagonal%3D%5Csqrt%7B2%7D%5Ctimes%20x)
Substituting the values we get
![x=\dfrac{8.44}{\sqrt{2}}=5.967\approx 5.97\ cm](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B8.44%7D%7B%5Csqrt%7B2%7D%7D%3D5.967%5Capprox%205.97%5C%20cm)
Therefore,
The value of x is 5.97 cm.