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

Given: length of rectangle = $40cm$

and, Breadth of the rectange $=22cm$

It is given that, Perimeter of rectangle $=$ Perimeter of square [Same wire is rebent]

$\therefore$ $2$ (Length $+$ Breadth) $=4\times$ Side

$\Rightarrow 2(40+22)=4\times$ Side

$\Rightarrow 2\times 62=4\times$Side

$\therefore$ Side $=\frac{124}{4}=31cm$

Area of rectangle $=$ length $\times$ breadth $=40\times 22=880c{m}^2$

Area of square $=(Side{)}^2=31\times 31=961c{m}^2$

Therefore, the square-shaped wire encloses more area.​​​​​​​​