Let the sides of a triangle are 3x, 4x and 5x.

Now, a = 3x, b = 4x and c = 5x

The perimeter 2s = 144

⇒ 3x + 4x + 5x = 144 [∵ a + b + c = 2s]

⇒ 12x = 144

⇒ x = 12

∴ sides of triangle are a = 3(x) = 36cm

b = 4(x) = 48 cm

c = 5(x) = 60 cm

Now semi perimeter s = 1/2 (a + b + c) = 1/2(144) = 72cm

Let l be the altitude corresponding to longest side,

∴ 1/2 × 60 × l = 864

Hence the altitude one corresponding long side = 28.8 cm