Question

Each side of a square is $45cm$ and a rectangle has length $50cm$. If the perimeters of both (square and rectangle) are same, find the breadth of the rectangle.

Answer 1

Calculating the perimeter of the square

Given,
Length of each side of the square $=45cm$
A square and a rectangle have equal perimeters.

The perimeter of the square is given by:
$P=4\left(Side\right)$
$P=4\left(45\right)$
$P=180cm$

Calculating the breadth of the rectangle

Since the perimeter of the square and rectangle is equal.
Thus,
The perimeter of the rectangle
$=$ the perimeter of the square
$=180cm$

Therefore, the perimeter of the rectangle is given by:
$P=2\left(\text{Length + Breadth}\right)$
$180=2(50+\text{Breadth})$
$180=100+2\times \text{Breadth}$
$180-100=2\times \text{Breadth}$
$80=2\times \text{Breadth}$
$\text{Breadth}=\frac{80}{2}=40cm$

Therefore, the breadth of the given rectangle is $40cm$.