Mathematics

# In the given figure, $AB$ and $DE$ are perpendicular to $BC$. If $AB=9cm, DE=3cm$ and $AC=24cm$, calculate $AD$.

$16cm$

##### SOLUTION
Given, $\angle ABC = \angle DEC= 90^{\circ}$
In $\triangle ABC$ and $\triangle DEC$,
$\angle ABC = \angle DEC$ (Each $90^{\circ}$)
$\angle ACB = \angle DCE$ (Common)
$\angle BAC = \angle CDE$ (third angle)
Thus, $\triangle ABC \sim \triangle DEC$
Hence, $\frac{AB}{DE} = \frac{AC}{DC}$
$\frac{9}{3} = \frac{24}{24 - AD}$
$24 - AD = 8$
$AD = 16$ cm

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Single Correct Medium Published on 09th 09, 2020
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