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

Let the sides of the triangle be 5x m, 12x m and 13x m.
We know:
Perimeter = Sum of all sides
or, 150 = 5x + 12x + 13x
or, 30x = 150
or, x = 5
Thus, we obtain the sides of the triangle.
5×">××5 = 25 m
12×">××5 = 60 m
13×">××5 = 65 m

Now,

Let:

$a=25 \mathrm{~m}, b=60 \mathrm{~m}$ and $c=65 \mathrm{~m}$

$\therefore s=\frac{150}{2}=75 \mathrm{~m}$

By Heron's formula, we have :

Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{75(75-25)(75-60)(75-65)}$

$=\sqrt{75 \times 50 \times 15 \times 10}$

$=\sqrt{15 \times 5 \times 5 \times 10 \times 15 \times 10}$

$=15 \times 5 \times 10$

$=750 \mathrm{~m}^{2}$