Question

A wire is in the shape of a square of side 5 m. It is later transformed into a rectangle(by bending) having a length of 7 m. Find the width of the rectangle?
m

Answer 1

Given, the side of the square $=5m$
Perimeter of the square $=4\times 5m=20m$

Square is bent into a rectangle of length 7m.
Let the width of the rectangle be $w$.
Perimeter of the rectangle $=2(\text{length + width)}$
$=2(7+w)m$

As length of the wire is constant, perimeter of both shapes would be same.
$\Rightarrow \text{Perimeter of the square = Perimeter of the rectangle}$
$\Rightarrow 20=2(7+w)$
Divide both sides by 2
$\Rightarrow \frac{20}{2}=\frac{2(7+w)}{2}$
$\Rightarrow 10=7+w$
Subtract 7 from both sides
$\Rightarrow 10-7=7+w-7$
$\Rightarrow 3=w$
$\Rightarrow w=3$

Hence, the width of the rectangle is $3$ m.