Question

The sides of a right triangular field are in the ratio $5:3:4$ and its perimeter is $180$ m. Find :

Altitude of the triangle corresponding to its largest side.

• A. $36$ m
• B. $30$ m
• C. $34$ m
• D. $32$ m

Answer 1

The correct option is A $36$ m

Let sides of a triangle be $5x,3x,4x$.

From Pythagoras theorem, $3^2+4^2=25=5^2$

Given, perimeter of triangle $=180m$

$\therefore$ perimeter of triangle$=180=3x+4x+5x$

$x=15$

Substituting value of $x$, we get

$a=45,b=60,c=75$

$\therefore$ Area of triangle $=\frac{45\cdot 60}{2}=1350m^2$

$\therefore \frac{base\cdot height}{2}=area=1350$

$\frac{75\cdot height}{2}=1350$

$\therefore$ height $=36m$