Question

ABCD is a parallelogram, $AE\perp DC$ and $CF\perp AD$. If $AB=16$ cm , $AE=8cm$ and $CF=10$ cm, find $AD$.

Answer 1

REF.image

Area of a parallelogram

=Base $\times$ Altitude.

For ABCD,

$\therefore AE\perp DC$

$\therefore$ AE is the altitude,DC is the base.

Area of a parallelogram $=Base\times Altitude$

$=DC\times AE$

$=AB\times AE$ (opp.sides of parallelogram are equal ).

$=16\times 8----\left(1\right)$

For ABCD,

$\therefore CF\perp AD$

$\therefore$ CF is the altitude AD is the base

Area of a parallelogram= $base\times Altitude$

$=AD\times CF$

$=AD\times 10----\left(2\right)$

From (1) & (2)

$16\times 8=AD\times 10$

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

$\Rightarrow AD=12.8cm$

$\therefore$ Thus,the length of AS is $12.8cm$.