Question

The ratio of two sides of a parallelogram is $3:4$. If its perimeter is $112cm$, find the length of all the sides of that parallelogram.

Answer 1

Let $ABCD$ be a parallelogram in which the ratio of sides $AB$ and $BC$ is $3:4$.
Thus, we have:
$AB=3x$ and $BC=4x$
We know that the opposite sides of a parallelogram are congruent.
$\therefore AD=BC=4x$ and $CD=AB=3x$

Perimeter of the parallelogram $=AB+BC+CD+DA$
$\Rightarrow 3x+4x+3x+4x=112$
$\Rightarrow 14x=112$
$\Rightarrow x=\frac{112}{14}$
$\Rightarrow x=8cm$
Thus, we get:
$AB=CD=3x=3\times 8cm=24cm$
$BC=AD=4x=4\times 8cm=32cm$
Therefore, the sides of the parallelogram are $24cm,32cm,24cm$ and $32cm$.