Question

In given figure, ABCD is a parallelogram. AE is perpendicular on DC and CF is perpendicular on AD.
If AB = 10 cm, AE = 8 cm and CF = 12 cm. Find AD.

Answer 1

In parallelogram $ABCD$, we have given $AB=10cm$, $AE=8cm$, and $CF=12cm$.

$\Rightarrow$ $AB=DC=10cm$ [Opposite sides of parallelogram are equal]

$\Rightarrow$ Lets find out area of parallelogram with height $AE$ and base $DC$.

$\Rightarrow$ Area of parallelogram $ABCD=b\times h$

$\Rightarrow$ Area of parallelogram $ABCD=DC\times AE$

$\Rightarrow$ $10\times 8$

$\therefore$ Area of parallelogram $ABCD=80c{m}^2$ --- ( 1 )

$\Rightarrow$ Now, to find area of parallelogram let $CF$ be the height and $AD$ will be base.

$\Rightarrow$ Area of parallelogram $ABCD=CF\times AD$

$\Rightarrow$ $80=12\times AD$ [From ( 1 )]

$\Rightarrow$ $AD=\frac{80}{12}$

$\therefore$ $AD=6.66cm$