Question

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

• A. $11.6cm$
• B. $12.8cm$
• C. $13.4cm$
• D. $14.8cm$

Answer 1

Answer: (B)

$12.8cm$

Area of parallelogram $=$ base $\times$ altitude

$1.)$ $AE\perp DC$, then

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

$=AB\times AE$ $[\because AB=DC=oppositesidesofparallelogram]$

$16\times 8=128\left(1\right)$

Now, $2.)CF\perp AD$, then

Area of parallelogram $ABCD$ $=AD\times CF=AD\times 10\left(2\right)$

From $\left(1\right),\left(2\right)$

$AD\times 10=128$
$\Rightarrow AD=\frac{128}{10}=12.8cm$