The base and height of a triangle are in the ratio 3 : 4 and its area is 216 cm². The height of the triangle is

Given:

Base: Height = 3: 4

Area = 216 cm²

Let,

Base = 3x

Height = 4x

We know that,

Area of a triangle = 1/2 × base × height

⇒ 216 = 1/2 × 3x × 4x

⇒ 216 × 2 = 12x²

⇒ 12 x² = 432

⇒ x² = 36

⇒ x = 6 cm

Therefore,

Height = 4x

= 24 cm