Question

In $\Delta ABC,\angle B={90}^{\circ }$ and $BD\perp AC$.

(iii) If $AC=9cm$ and $AB=7cm$; find $AD$.

Answer 1

Step : Finding the length of $AD$

Given : $\angle B={90}^{\circ }$ and $BD\perp AC,AC=9cm$ and $AB=7cm$.

In $\Delta ABC$ and $\Delta ADB$,



$\angle A=\angle A$ [Common angle]

$\angle ABC=\angle ADB$ [ Both are ${90}^{\circ }$ ]

By $AA$ criterion; $\Delta ABC\sim \Delta ADB$

$\Rightarrow \frac{AB}{AD}=\frac{BC}{DB}=\frac{AC}{AB}$

[Corresponding sides of similar triangles are in proportion]

Consider $\frac{AB}{AD}=\frac{AC}{AB}$

$\Rightarrow A{B}^2=AD\times AC$

$\Rightarrow 7^2=AD\times 9$

$\Rightarrow AD=\frac{49}{9}cm$

Hence, length of $AD$ is $\frac{49}{9}cm$.