The length of the sides of a triangle are in the ratio 3:4::5 and its perimeter is 144 cm. Find the area of the triagnle and the height corresponding to the longest side.
Given, the length of sides of the triangle is the ratio 3 : 4 : 5.
and perimeter = 144cm
⇒ 3x + 4x + 5x =144
⇒ 12x =144
⇒ x =12cm
∴ shortest side = 3x = 3 ×12 = 36cm
side of medium length = 4x = 4 × 12 = 48cm
longest side = 5x = 5 ×12 = 60cm
Again s = semi-perimeter of Δ = = 72cm
Using, heron's formula, area of Δ
Equating (1) and (2), we get
Hence, the height of triangle corresponding to longest side is 28.8 cm.