Question

In the above figure, $ABCD$ is a parallelogram, $AE\perp DC$ and $CF\perp AD$. If $AB=16cm,AE=8cm$ and $CF=10cm$, Find $AD.$

• A. $AD=12.8cm$
• B. $AD=13.8cm$
• C. $AD=14.8cm$
• D. $AD=11.8cm$

Answer 1

Answer: (A)

$AD=12.8cm$

$\Rightarrow$ $AB=16cm,AE=8cm$ and $CF=10cm$ [ Given ]

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

$=16\times 8$

$=128c{m}^2$ ----- ( 1 )

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

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

Comparing ( 1 ) and ( 2 ) we get,

$\Rightarrow$ $AD\times 10=128$

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

$\Rightarrow$ $AD=12.8cm$