Question

If the adjacent sides of a parallelogram are in the ratio $2:3$ and the sum of all the sides is $50cm$, find the measure of the sides of the parallelogram.

Answer 1

The opposite sides of a parallelogram are equal.

Let one of the sides be $a$ and adjacent side be $b$.

Given :

$2a+2b=50$

$\Rightarrow a+b=25$ $......\left(1\right)$

Also $a:b=2:3$ $......\left(2\right)$

$\Rightarrow a=\frac{2b}{3}$ $.....\left(3\right)$

Substituting $\left(3\right)$ in $\left(1\right)$ we get

$\frac{2b}{3}+b=25$

$\frac{5b}{3}=25$

$b=15cm$

$\therefore a=10cm\dots \left(3\right)$

$\therefore$ if $ABCD$ is the parallelogram, then the length of the sides of the parallelogram are:

$AB=CD=10cm$

$BC=AD=15cm$

Hence, solved.