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Q.
The sides of a triangle are $45 cm , 60 cm$ and $75 cm$. Find the length of the altitude drawn to the longest side from its opposite vertex (in cm).
Mensuration
Solution:
$45^2+60^2=75^2$, the triangle is right angled.
$\therefore$ Its hypotenuse is $75 cm$.
Its perpendicular sides are $45 cm$ and $60 cm$.
$\therefore \text { Its area }=\frac{(45)(60)}{2} cm ^2$
Let the required altitude be $/ cm$
$\therefore \text { Longest side }=\text { Hypotenuse }=75 cm$
$\frac{(45)(60)}{2}=\frac{(75)(h)}{2}$
$\therefore h=36 cm .$