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

Correct option is A

Given:

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

The ratio of their heights is 3:4.

Formula Used:

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

Solution:​

Let the areas of the two triangles be $$A_1$$​ and $$A_2$$​, their bases be $$b_1$$​ and $$b_2$$​, and their heights be $$h_1$$​ and $$h_2$$​.

Then, the ratio of the areas of the triangles can be expressed as:

​$$\frac{A_1}{A_2} = \frac{\frac{1}{2} \times b_1 \times h_1}{\frac{1}{2} \times b_2 \times h_2} = \frac{b_1 \times h_1}{b_2 \times h_2}$$​​

Given that:

​$$\frac{A_1}{A_2} = \frac{4}{3}, \quad \frac{h_1}{h_2} = \frac{3}{4}$$​​

Using the given ratio of areas:

​$$\frac{4}{3} = \frac{b_1 \times3}{b_2 \times 4} \\ \ \\\frac{16}{3} = \frac{3 \times b_1}{b_2} \\ \ \\\frac{b_1}{b_2} = \frac{16}{9}$$​​

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