Question

The sides of a triangle are $45cm,60cm$ and $75cm$. Find the length of the altitude drawn to the longest side from its opposite vertex (in cm).

• A. 27
• B. 21
• C. 39
• D. 36

Answer 1

Answer: (D)

$45^2+60^2=75^2$, the triangle is right angled.
$\therefore$ Its hypotenuse is $75cm$.
Its perpendicular sides are $45cm$ and $60cm$.
$\therefore \text{ Its area }=\frac{(45)(60)}{2}c{m}^2$
Let the required altitude be $/cm$
$\therefore \text{ Longest side }=\text{ Hypotenuse }=75cm$
$\frac{(45)(60)}{2}=\frac{(75)(h)}{2}$
$\therefore h=36cm.$