The length of the sides of a triangle are in the ratio 4:5:3 and its perimeter is 96cm. Find it’s area.

As the length of the side is in the ratio 4:5:3.

Let the sides be a, b and c whose lengths be 4k, 5k and 3k respectively. (Where k is some arbitrary constant).

Now Perimeter of triangle = 96 cm.

∴ we get 4k + 5k + 3k = 96

⇒ 12 k = 96

⇒ k = ⇒ k = 8.

∴ Sides become a = 4k = 4 × 8 = 32cm

b = 5k = 5 × 8 = 40cm

c = 3k = 3 × 8 = 24 cm

∴ We get sides a, b, c as 32 cm, 40 cm and 24 cm respectively.

∴ Now we need to find area of triangle with sides 32cm, 40cm and 24cm.

∴ by Heron’s formula we get area of triangle

=

(where s = s is called as the semi perimeter )…(1)

∴ we get

Substituting value of s, a, b and c in equation 1 we get

⇒

=

=

∴ The area of triangle is 384cm².