Question

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

Answer 1

Let $a$ be the side of a square, $l$ be the length and $b$ be the breadth of rectangle.

As length of wire is constant, perimeter of both shapes would be same,

$\Rightarrow 4a=2(l+b)$

$\Rightarrow 40=2(12+b)$

$\Rightarrow b=18$ cm

Area of square$=a^2={10}^2=100c{m}^2$

Area of rectangle$=lb=12\times 18=216c{m}^2$

$\Rightarrow$ Area of rectangle is greater by $116c{m}^2$.