The ratio of the areas of two triangles is 4 : 3 and the ratio of their heights is 3 : 4. Find the ratio of their bases.

Correct option is C

Given:

The ratio of the areas of two triangles is 4:3.

The ratio of their heights is 3:4.

Concept Used:

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

Solution:
Let the bases of the two triangles be $$B_1$$​ and $$B_2,$$​ and the heights be $$H_1$$​ and $$H_2$$​.
From the given,

​$$\frac{\text{Area}_1}{\text{Area}_2} = \frac{4}{3}, \quad \frac{H_1}{H_2} = \frac{3}{4}$$

$$\frac{\text{Area}_1}{\text{Area}_2} = \frac{\frac{1}{2} B_1 H_1}{\frac{1}{2} B_2 H_2} = \frac{B_1 H_1}{B_2 H_2}$$​​

​$$\frac{B_1}{B_2} \times \frac{3}{4} = \frac{4}{3}$$​​

​$$\frac{B_1}{B_2} = \frac{4}{3} \times \frac{4}{3} = \frac{16}{9}$$​​

Thus, the ratio of the bases is 16:9.