Question

If the perimeter of a parallelogram is 140 m, the distance between a pair of opposite sides is 7 m and its area is 210 square m, find the length of two adjacent sides of the parallelogram.

Answer 1

Given that,

The perimeter of the parallelogram is $140m$.

Its area is $210m^2$

Distance between a pair of opposite sides is $7m$.

To find out,

Length of the two adjacent sides of the parallelogram.

Let $a,b$ be the two adjacent sides of the parallelogram, as shown in the figure above.

We know that, area of a parallelogram $=side\times itscorrespondingheight$

So, if $a$ is the side, $h$ will be its corresponding height.

Here, $h=7m$

Hence, $a\times h=210$

$\Rightarrow a=\frac{210}{7}$

$=30m$

We also know that, perimeter of a parallelogram $=2(a+b)$

Here, perimeter $=140m,a=30m$

Hence, $2(30+b)=140$

$\Rightarrow 60+2b=140$

$\Rightarrow 2b=80$

$\Rightarrow b=40m$

Hence, the two adjacent sides of the parallelogram are $30m$ and $40m$.