Question

In Figure given below, $ABCD$ is a parallelogram, $DL\perp AB$ and $DM\perp BC.$ If $AB=18cm,$ $BC=12cm$ and $DM=9.3cm,$ find $DL.$

Answer 1

We have,
Taking $BC$ as the base, we have

$BC=12cm$ and altitude $DM=9.3cm$

$\therefore$ Area of parallelogram $ABCD=$ Base $\times$Altitude

$=(12\times 9.3)=111.6c{m}^2\dots \dots \left(i\right)$

Now, Taking $AB$ as the base, we have

Area of the parallelogram $ABCD=$ Base $\times$ Altitude $=(18\times DL)\dots \dots \left(ii\right)$

From equation $\left(i\right)$ and $\left(ii\right),$ we have

$18\times DL=111.6c{m}^2$

$\Rightarrow DL=\frac{111.6}{18}cm=6.2cm$