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

Given: Ratio of Sides = 5 : 12 : 13

Perimeter = 150 cm

Let the sides be,

a = 5x cm

b = 12x cm

c = 13x cm

We know that,

Perimeter of a triangle = a + b + c

⇒ 150 cm = 5x cm + 12x cm + 13x cm

⇒ 150 cm = 30x cm

⇒ x = 5

Therefore,

a = 5x cm = 5 × 5 cm = 25 cm

b = 12x cm = 12 × 5 cm = 60 cm

c = 13x cm = 13 × 5 cm = 65 cm

Now,

We know that,

Area of a scalene triangle = √(s(s-a)(s-b)(s-c))

Where,

⇒ s = 75cm

Now,

Area of a scalene triangle = √(75cm × (75-25)cm × (75-60)cm × (75-65)cm)

= √(75cm × 50cm × 15cm × 10cm)

= √562500 cm²

= 750 cm²