In a right - angled triangle, base is $12\ cm$ and hypotenuse is $15\ cm$. Find the Perpendicular.

Given: In a right triangle, hypotenuse$=15\ cm$ and base$=12\ cm$.
 

To do: to find the length of Perpendicular.

Solution:

Using Pythagoras theorem,

$( Hypotenuse)^{2}=( Base)^{2}+( Perpendicular)^{2}$

 [On substituting the given value of hypotenuse and base.]

$\Rightarrow ( 15)^{2}=( 12)^{2}+( Perpendicular)^{2}$

$\Rightarrow 225=144+( Perpendicular)^{2}$

$\Rightarrow ( Perpendicular)^{2}=225-144$

$\Rightarrow ( Perpendicular)^{2}=81$

$\Rightarrow Perpendicular=\sqrt{81}$

$\Rightarrow Perpendicular=\pm9$

$\because$ Length can't be negative, therefor we reject the value $Perpendicular=-9$

$\therefore$ Length of the $Perpendicular=9\ cm$.

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Updated on: 10-Oct-2022

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