The ratio of bases of two triangles is 4 : 5 and that of their areas is 8 : 15. What is the ratio of their corresponding altitudes?

Correct option is B

Given:

Ratio of bases of two triangles = 4 : 5

Ratio of areas of the two triangles = 8 : 15

Formula Used:

Area =$$\frac{1}{2} \times \text{base} \times \text{altitude}$$​

Solution:
Let the bases of the two triangles be $$b_1$$​ and $$b_2$$​, and the corresponding altitudes be $$h_1$$​ and $$h_2.$$​​

​$$\frac{b_1}{b_2} = \frac{4}{5} \quad \text{and} \quad \frac{A_1}{A_2} = \frac{8}{15}$$​​

From the formula for the ratio of areas:

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

​$$\frac{8}{15} = \frac{4}{5} \times \frac{h_1}{h_2}$$​​

​$$\frac{h_1}{h_2} = \frac{8}{15} \times \frac{5}{4} = \frac{40}{60} = \frac{2}{3}$$​

Thus, the ratio of their corresponding altitudes is 2 : 3.