Question

Consider a parallelogram, $\mathrm{ABCD}$. $\mathrm{AE}$ is perpendicular to $\mathrm{DC}$ and $\mathrm{CF}$ is perpendicular to $\mathrm{AD}$. If $\mathrm{AB}$ $=16\mathrm{cm}$, $\mathrm{AE}$ $=8\mathrm{cm}$, and $\mathrm{CF}$$=10\mathrm{cm}$, find $\mathrm{AD}$.

Answer 1

Use the formula of area of parallelogram

In parallelogram $\mathrm{ABCD}$, $\mathrm{AE}$ $=8\mathrm{cm}$, $\mathrm{AB}$ $=16\mathrm{cm}$ and $\mathrm{CF}$ $=10\mathrm{cm}$

In a parallelogram, we know that opposite sides are equal.

Therefore, $\mathrm{CD}=\mathrm{AB}$ $=$ $16\mathrm{cm}$

To find the value of $\mathrm{AD}$,

We know that area of parallelogram is given by

Area of parallelogram $=$ $\mathrm{base}\times \mathrm{height}$

$\Rightarrow$$CD\times AE=AD\times CF$

$\Rightarrow$ $16\times 8=\mathrm{AD}\times 10$

$\Rightarrow$ $128=10\mathrm{AD}$

$\Rightarrow$ $\mathrm{AD}=12.8\mathrm{cm}$

Hence, length of $\mathrm{AD}$ is $12.8\mathrm{cm}$.