Let the sides of the given triangle be 5x, 12x and 13x

Given,

Perimeter of the triangle = 150m

Perimeter of the triangle = (5x + 12x + 13x)

150 = 30x

Therefore,

x =

Thus,

Sides of the triangle are:

5x = 5 × 5 = 25 m

12x = 12 × 5 = 60 m

13x = 13 × 5 = 65 m

Let,

a = 25 m, b = 60 m and c = 65 m

Therefore,

s =

=

=

= 75 m

We know that,

Area of triangle =

=

=

=

=

= 25 × 5 × 3 × 2

= 750 sq m

Hence, area of triangle is 750 sq m.