Since length of diagonal ( [tex]Diagonal= 9.9cm[/tex] ) is less than diameter of circle ( 11 cm ) , Therefore , the square will fit inside the circle without touching the edge of the circle.
Step-by-step explanation:
Here we have , A circle has diameter of 11 cm A square has side length of 7 cm . Use Pythagoras’ Theorem to show that the square will fit inside the circle without touching the edge of the circle . Let's find out:
We know the concept that for any square to fit inside the circle without touching the edge of circle , diagonal of square must be less than diameter of circle . Let's find out length of diagonal by using Pythagoras Theorem :
[tex]Hypotenuse ^2 = Perpendicular^2+Base^2[/tex]
For a square , [tex]Perpendicular = base = side[/tex]
⇒ [tex]Diagonal^2 = 2(side)^2[/tex]
⇒ [tex]Diagonal= \sqrt{2}(side)[/tex]
⇒ [tex]Diagonal= \sqrt{2}(7)[/tex]
⇒ [tex]Diagonal= 9.9cm[/tex]
Since length of diagonal ( [tex]Diagonal= 9.9cm[/tex] ) is less than diameter of circle ( 11 cm ) , Therefore , the square will fit inside the circle without ruching the edge of the circle.
