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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