Give that the ratio of altitudes of two triangles is 4 : 5, ratio of their areas is 3: 2. The ratio of their corresponding bases is

Given that ratio of altitudes of two triangles is 4:5

=> $$\frac{h_{1}}{h_{2}}$$=$$\frac{4}{5}$$

Also, Given that, ratio of areas of two triangles is 3:2

=> $$\frac{\frac{1}{2} \times b_{1} \times h_{1}}{\frac{1}{2} \times b_{2} \times h_{2}}$$ = $$\frac{3}{2}$$

=> $$\frac{b_{1} \times 4}{ b_{2} \times 5}$$ = $$\frac{3}{2}$$

=> $$\frac{b_{1}}{ b_{2}}$$ = $$\frac{15}{8}$$

Therefore, ratios of the bases is 15:8