Question

The sides of a triangle are in the ratio $5:12:13$, and its perimeter is $150m$. Find the area of the triangle.

Answer 1

Let the sides of the triangle be $5x,12x,13x$ where $x$ is a positive rational number.

$\therefore$ Perimeter $=5x+12x+13x=150$

$\Rightarrow 30x=150$

$\Rightarrow x=\frac{150}{30}$

$\Rightarrow x=5$

Hence, the sides of the triangle are $25m,60m,65m$

Also, these sides form a Pythagoras Triplet, as

${25}^2+{60}^2=625+3600=4225={65}^2$

Hence, the triangle is a right angles triangle whose hypotenuse is $65m$.

So, area of triangle $=\frac{1}{2}\times \text{base}\times \text{height}$

$=\frac{1}{2}\times 25\times 60$

$=750sq.units$