Question

One side of a parallelogram is $2.5m$ longer than its adjacent side. If the perimeter of the parallelogram is $51m$, find the measure of all its sides.

Answer 1

Let ABCD is a parallelogram

Let $AB=xm$

Adjacent side $BC=(x+2.5)m$

Now,

$CD=AB=xm$ [Opposite sides of parallelogram are equal]

And $AD=BC=(x+2.5)m$ [Opposite sides of parallelogram are equal]

Perimeter $=AB+BC+CD+AD$

$\Rightarrow 51=x+x+2.5+x+x+2.5$

$\Rightarrow 51=4x+5$

$\Rightarrow 4x=51-5$

$\Rightarrow 4x=46$

$\Rightarrow x=\frac{46}{4}$

$\Rightarrow x=11.5m$

So,

$AB=CD=11.5m$

and $BC=AD=11.5+2.5=14m$