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

Correct option is B

Given:

The ratio of base to height = 3:4

Area of the triangle = 216 cm²

Concept Used:

A = $$\frac{1}{2} \times \text{Base} \times \text{Height}$$​

Solution:

216 = $$\frac{1}{2} \times (3x) \times (4x)$$​

216 = $$\frac{1}{2} \times 12x^2$$​

216 $$\times 2 = 12x^2$$​

432 = 12x$$^2$$​

x$$^2 = \frac{432}{12}$$​

x^2 = 36

x = $$\sqrt{36}$$​ = 6

Thus, the height is

4x = 4 × 6 = 24 cm

$$\boxed{24 \text{ cm}}$$​