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In figure below, $ \mathrm{ABCD} $ is a parallelogram, $ \mathrm{AE} \perp \mathrm{DC} $ and $ \mathrm{CF} \perp \mathrm{AD} $. If $ \mathrm{AB}=16 \mathrm{~cm}, \mathrm{AE}=8 \mathrm{~cm} $ and $ \mathrm{CF}=10 \mathrm{~cm} $, find $ \mathrm{AD} $.
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Academic Mathematics NCERT Class 9

Given:

$ABCD$ is a parallelogram, $AE \perp DC$ and $CF \perp AD$.

$AB = 16\ cm, AE = 8\ cm$ and $CF = 10\ cm$.

To do:

We have to find $AD$.

Solution:

We know that,

Area of a parallelogram $=$ Base $\times$ Altitude

Therefore,

Area of parallelogram $ABCD = AB \times AE$

$= 16 \times 8$

$= 128\ cm^2$

Now,

Altitude $CF = 10\ cm$

This implies,

Area $=$ Base $(AD)\times$ Altitude$(CF)$

$128 = 10 \times AD$

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

$AD = 12.8\ cm$

Hence, $AD = 12.8\ cm$.

Simply Easy Learning

Updated on: 10-Oct-2022

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