Question

The lengths of the sides of a triangle are in the ratio $3:4:5$. Find the area of the triangle if its perimeter is $144cm$.

• A. $864$ sq. cm
• B. $874$ sq. cm
• C. $854$ sq. cm
• D. $884$ sq. cm

Answer 1

The correct option is A $864$ sq. cm

Given, Side of triangle are in ratio $3:4:5$ and their perimeter $144cm$.
Let the sides of triangle be $3x,4x,5x$
Perimeter $=3x+4x+5x=144cm$
$12x=144$
$\therefore x=12$
Then sides of triangle are $3x=3\times 12=36cm$,
$4x=4\times 12=48cm$,
$5x=5\times 12=60cm$.
Now, Semi perimeter, $s=\frac{\text{Sum of sides of triangle}}{2}=\frac{36+48+60}{2}=72cm$
Using Heron's formula, Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{72(72-36)(72-48)(72-60)}=\sqrt{72\times 36\times 24\times 12}=864{cm}^2$