# ∆ABC is right angled at $A$ $(Fig\ 11.25)$. $AD$ is perpendicular to $BC$. If $AB = 5\ cm,\ BC = 13\ cm$ and $AC = 12\ cm$, Find the area of $∆ABC$. Also find the length of $AD$."

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Given: ∆ABC is right angled at $A$ $(Fig\ 11.25)$. $AD$ is perpendicular to $BC$. If $AB = 5\ cm,\ BC = 13\ cm$ and $AC = 12\ cm$.

To do: To find the area of $∆ABC$ and also find the length of $AD$.

Solution:

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

$=\frac{1}{2}\times5\times12$

$=30\ cm^2$

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

$30cm^2=\frac{1}{2}\times13cm\times AD$

$AD=\frac{30\times2}{13}\ cm$

$=\frac{60}{13}\ cm$

$=4.62\ cm$
Updated on 10-Oct-2022 13:35:58