Question

A wire in the form of a circle with radius 42 cm.
It is bent into a square . Find the sides of square.

Answer 1

Given :-

A wire in the form of a circle with radius 42 cm is bent into a square

Required to find :-

• Side of the square ?

Formulae used :-

$\large{\rightarrowtail{\boxed{\rm{ Perimeter \; of \; a \; circle = 2\pi r }}}}$

$\large{\rightarrowtail{\boxed{\rm{ Perimeter \; of \; a \; square = 4 \times Side }}}}$

Solution :-

Given that :-

A wire in the form of a circle with radius 42 cm is bent into a square .

We need to find the length of side of the square .

So,

Consider the statement 1 .

Here,

Radius = 42 cm

using the formula ,

$\large{\rightarrowtail{\boxed{\rm{ Perimeter \; of \;a \; circle = 2\pi r }}}}$

So,

$\rightarrow{\rm{ Perimeter = 2 \times \dfrac{22}{7} \times 42 }}$

$\rightarrow{\rm{ Perimeter = 2 \times 22 \times 6 }}$

$\rightarrow{\rm{ Perimeter = 264 \; cm }}$

Hence,

Perimeter of the circle = 264 cm

But ,

It is mentioned that the wire which is in form of a circle was bent to make a square .

So,

This concludes the fact that :-

Perimeter of the circle = Perimeter of the Square

Hence,

Perimeter of the Square = 264 cm

However,

Let the measurement of side be " x " cm

So,

Using the formula

$\large{\rightarrowtail{\boxed{\rm{ Perimeter \; of \; a \; square = 4 \times Side }}}}$

$\leadsto{\tt{ 4 \times x = 264 }}$

$\leadsto{\tt{ 4x = 264 }}$

$\leadsto{\tt{ x = \dfrac{264}{4}}}$

$\leadsto{\tt{ x = 66 \; cm }}$

$\Large{\dagger{\boxed{\sf{ Side \; of \; the \; square = 66 \; cm }}}}$

Answer 2

Given ,

A wire in the form of circle of radius 42 cm is bent into the shape of square

It implies that ,

$\large \sf \fbox{Perimeter \: of \: circle = Perimeter \: of \: square }$

Let , the perimeter of square be " x "

Thus ,

$\sf \Rightarrow 2 \times \frac{22}{ \cancel{7}} \times \cancel{42} = 4x \\ \\\sf \Rightarrow 44 \times 6 = 4x \\ \\ \sf \Rightarrow x = 11 \times 6 \\ \\\sf \Rightarrow x = 66 \: \: cm$

$\therefore{ \sf \bold{ \underline{The \: side \: of \: square \: is \: 66 \: cm}}}$