Question

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

Answer 1

If the same wire is used then,

Perimeter of square = Perimeter of rectangle

$\Rightarrow 4\times side=2(l+b)$

$\Rightarrow 4\left(10\right)=2(12+b)$

$\Rightarrow 40=24+2b$

$\Rightarrow b=8\text{cm}$

So, breadth of rectangle is $8\text{cm}$.

Area of square = ${\left(\text{side}\right)}^2$

$=(10{)}^2$

$=100{\text{cm}}^2$

Area of rectangle = $l\times b$

= $12\times 8$

= $96{\text{cm}}^2$

Thus, area of square is larger by $100-96=4{\text{cm}}^2$