Question

A wire is in the shape of a square of side $10cm$. If the wire is rebent into a rectangle of length $12cm$, find its breadth. Which figure encloses more area and by how much?

Answer 1

Given, side of the square $=10cm$
Length of the wire $=$ Perimeter of the square $=4\times$ Side
$=4\times 10cm=40cm$
Length of the rectangle $\left(l\right)=12cm$
Let $b$ be the breadth of the rectangle.
Perimeter of the rectangle $=$ Perimeter of the square
$\Rightarrow 2(l+b)=40$
$\Rightarrow 2(12+b)=40$
$\Rightarrow 24+2b=40$
$\Rightarrow 2b=40-24$
$\Rightarrow b=\frac{16}{2}$
$\therefore b=8$
Thus, Breadth of the rectangle $=8cm$
Now, Area of the square $={\text{(Side)}}^2=(10cm\times 10cm)$
$=100c{m}^2$
Area of the rectangle $=l\times b$
$=12\times 8$
$=96c{m}^2$

Hence, the square encloses more area.
It encloses $4c{m}^2$ more area.