Question

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

Answer 1

let the sides be x
3x+4x+5x=144cm
12x=144cm
x=144/12
x=12cm
3x=36cm
4x=48cm
5x=60cm
now find the semi perimeter
144/2=72cm
$\sqrt S(S-a)(S-b)(s-c)$
s is the semiperimeter 
then simplify them to get the the answer

Answer 2

Let the length of each side be 3x cm, 4x cm and 5x cm respectively
perimeter = (3x +4x + 5x)
144 = 12x
x = 12
Sides of triangle are 36cm, 48cm, 60cm respectively.
let p = half of perimeter = 72
area = sqrt[p(p-a)(p-b)(p-c)] = sqrt[72*36*24*12] = sqrt[746496] = 864 cm^2