Question

• Two adjacent sides of a parallelogram are $24cm$ and $18cm$ if the distance between the longer side is $12cm$, find the distance between the shorter side.

Answer 1

• Step 1: Finding the area of the parallelogram.

Two adjacent sides of the parallelogram are $AB=24cm$ and $BC=18cm$and the distance between the longer side, $DE=12cm.$

The distance between the shorter side has to be found.

Let the distance between the shorter side, $DF$ be $xcm$

Area of the parallelogram $=Base\times Height$

Area of the parallelogram, considering AB as the base $=AB\times DE$

$=24\times 12$

$Area=288c{m}^2$

• Step 2: Finding the sides of the parallelogram.

Now considering BC as the base, the area of the parallelogram $=BC\times DF$

$=18\times x$

$Area=18x$

Since the area of the parallelogram will be the same, if we consider $AB$ as the base or $BC$ as the base.

$\begin{array}{rcl}So,AB\times DE& =& BC\times DF\\ & \Rightarrow & 288=18x\\ x& =& \frac{288}{18}\\ x& =& 16cm\end{array}$

So, the distance between the shorter side is $16cm$.