Question

A wire is in the shape of a square of side $10cm$. If the wire is bent and made into a rectangle of length $12cm$, what is its breadth?

Answer 1

Step $1$ : Finding the perimeter of sqaure:

Given, Side of the square: $10cm$

Hence, Perimeter of the square$=4\times 10=40cm$ $=$ Length of the wire.

Step $2$ : Finding the perimeter of rectangle :

Given, Length of the rectangle $=$$12cm$

Let the breadth of the rectangle be $b$

Since the square is stretched to make a rectangle this means, the perimeter of both the rectangle and the square will be same,

We know that the Perimeter of rectangle $$\begin{gathered} =2(\mathrm{length}+\mathrm{breadth}) \\ =2(12+b) \\ =24+2\mathrm{b} \end{gathered}$$

Step $3$ : Calculation to find breadth of rectangle:

Since, perimeter of rectangle$=$ perimeter of square

$$\begin{gathered} \Rightarrow 24+2\mathrm{b}=40 \\ \Rightarrow 2\mathrm{b}=40-24 \\ \Rightarrow 2\mathrm{b}=16 \\ \Rightarrow \mathrm{b}=8 \end{gathered}$$

Hence, breadth of rectangle$=8cm$