Question

A wire is in the shape of a rectangle. Its length is $40cm$ and breadth is $22cm.$ If the same wire is rebent in the shape of a square, what will be the measure of each side? Also, find which shape encloses more area?

Answer 1

The length of the rectangle $=40cm$

The breadth of the square $=22cm$

Step 1: find the side of the square.

The perimeter of the square is the same as the perimeter of a rectangle

$\therefore$ The perimeter of the rectangle = Perimeter of the Square

$2(Length+Breadth)=4xsideofthesquare$

$$\begin{gathered} 2(Length+Breadth)=4\times side \\ 2(40+22)=4\times side \\ 2\left(62\right)=4\times side \\ 124=4\times side \\ \therefore Side=\frac{124}{4} \\ Side=31cm \end{gathered}$$

Step 2: Find the area of the given figures.

The area of the rectangle is given by$=(Length\times Breadth)$

$$\begin{gathered} =40\times 22 \\ =880c{m}^2 \end{gathered}$$

Area of square $=side\times side$

$$\begin{gathered} =31\times 31 \\ =961c{m}^2 \end{gathered}$$

Therefore, a square-shaped wire encloses more area.

Hence, the measure of each side of the square is $31cm$and square-shaped wired encloses more area than rectangle-shaped wired.