The sides of a triangle are in the ratio 13: 14: 15 and its perimeter is 84 cm. Find the area of the triangle.

It is given in the question that,

Perimeter of triangle = 84 cm

Also, sides or triangle are: in ratio 13: 14: 15

Let, a = 13x

b = 14x

c = 15x

We know that,

Perimeter of triangle = Sum of all sides

84 = a + b + c

84 = 13x + 14x + 15x

84 = 42x

x =

x = 2 cm

Thus, a = 13 × 2 = 26 cm

b = 14 × 2 = 28 cm

c = 15 × 2 = 30 cm

∴ s =

=

= 42 cm

Hence,

Area of triangle =

=

=

= 336 cm^{2}

6