In a parallelogram  $ABCD, AB=15 cm$. The altitudes correspond to the sides $AB$ and $AD$ are respectively $7 cm$ and $8 cm$. Find  $AD$:

 

We know that the formula for finding the area of a parallelogram is ,$Area = base \times height$

Here, in the parallelogram is ABCD.

 $AB=15 cm$.

The altitudes corresponding to the sides $AB$ and  $AD$ are respectively $7 cm$ and  $8 cm$.

By the formula for the area of a parallelogram,  $\frac{1}{2}\times AB\times altitud{e}_1=\frac{1}{2}\times AD\times Altitud{e}_2$

$\Rightarrow AB\times altitud{e}_1=AD\times Altitud{e}_2$ 

$\Rightarrow 15\times 7=AD\times 8$

$\Rightarrow AD=\frac{105}{8}=13.125 cm$

Hence, the length of AD is $13.125 cm$.