Question

Find all the possible dimensions (in natural numbers) of a rectangle with a perimeter $36cm$ and find their areas.

Answer 1

Perimeter of the rectangle $=36cm$
$\Rightarrow 2\times (length+breadth)=36cm$
$\Rightarrow (length+breadth)=\frac{36}{2}cm=18cm$
$\therefore$ The possible dimension of the rectangle and their area as follows:

Dimension	Area
$1cm\times 17cm$	$17c{m}^2$
$2cm\times 16cm$	$32c{m}^2$
$3cm\times 15cm$	$45c{m}^2$
$4cm\times 14cm$	$56c{m}^2$
$5cm\times 13cm$	$65c{m}^2$
$6cm\times 12cm$	$72c{m}^2$
$7cm\times 11cm$	$77c{m}^2$
$8cm\times 10cm$	$80c{m}^2$
$9cm\times 9cm$	$81c{m}^2$