Question

In $△ABC,\angle BAC={90}^o,AD\perp BC,BD=4cm,DC=5cm$, Find x and y.

Answer 1

It is given that $\angle BAC={90}^0$ and $AD\perp BC$

Also, $△ABD$ and $△CBD$ are similar right angled triangle, thus with $AD=y$ cm, $BC=5$ cm and $DC=5$ cm, we have,

$A{D}^2=BC\times DC\Rightarrow y^2=4\times 5\Rightarrow y^2=20\Rightarrow y=\sqrt{20}\Rightarrow y=2\sqrt{5}$

Similarly, $△ABC$ and $△DBA$ are similar right angled triangle, thus with $AB=x$ cm, $BC=9$ cm and $BD=4$ cm, we have,

$A{B}^2=BC\times BD\Rightarrow x^2=9\times 4\Rightarrow x^2=36\Rightarrow x=\sqrt{36}\Rightarrow x=6$

Hence, $x=6$ cm and $y=2\sqrt{5}$ cm.