Question

In parallelogram ABCD, AB = 10 cm. The altitudes corresponding to the sides AB and AD are respectively 7 cm and 8 cm. Find AD.

Answer 1

We have,
$\text{Area of a}|{|}^{gm}=\text{Base}\times \text{Height.}$
$\therefore ar\left(ABCD\right)=AB\times DM$
$=(10\times 7){\text{cm}}^2....\left(i\right)$
$\text{Also,}ar\left(ABCD\right)=AD\times BN$
$=(AD\times 8){\text{cm}}^2....\left(ii\right)$

From (i) and (ii), we get
$10\times 7=AD\times 8$
$\Rightarrow AD=\frac{10\times 7}{8}\text{cm}=8.75\text{cm}.$