Question

In triangle ABC , angle A = 90 degree , AB = 5 cm, BC= 13 cm nd AD perpendicular BC. Then the length of AD is

Answer 1

The length of $AD$ is $4.61\ cm$

Step-by-step explanation:

Given,

In $\triangle ABC$,$\angle A = 90\ degree,AB=5\ cm,BC=13\ cm$ and $AD \perp BC$

From figure,

$AC^{2} =BC^{2}-AB^{2}$ (∵ $\triangle ABC$ is right-angle triangle )

⇒$AC=\sqrt{13^{2}-5^{2}}$

⇒$AC=12\ cm$

If we consider $AB$ as base,

Then Area of triangle $\triangle ABC=\frac{1}{2}\times AB\times AC$

                                                $=\frac{1}{2}\times 5\times 12$

                                               $=30\ cm^{2}$

Consider $BC$ as base,

Then Area of triangle $\triangle ABC=\frac{1}{2}\times BC\times AD$

∴ $\frac{1}{2}\times BC\times AD=30$

⇒$BC\times AD=60$

⇒$AD=\frac{60}{13}$

∴ $AD=4.61$ $cm$

So, The length of $AD$ is $4.61\ cm$