Question

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

• A. $16cm$
• B. $17cm$
• C. $18cm$
• D. $19cm$

Answer 1

The correct option is A $16cm$

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