The ratio of the areas of two triangles ABC and PQR is 3 : 5 and the ratio of their heights is 5 : 3. The ratio of the bases of triangle ABC to that of triangle PQR is:

Let the Areas  of $$\triangle ABC$$ and $$\triangle PQR$$  are  $$3x:5x$$ 

Let the Heights  of $$\triangle ABC$$ and $$\triangle PQR$$  are  $$5y:3y$$  and Bases are $$B_{1}$$ and $$B_{2}$$ respectively.

Area of $$\triangle ABC$$ = $$\frac{1}{2} \times 5y\times B_{1}$$ and Area of $$\triangle PQR$$ = $$\frac{1}{2} \times3y\times B_{2}$$

$$\therefore \frac{3x}{5x} = \frac{\frac{1}{2} \times 5y\times B_{1}}{\frac{1}{2} \times3y\times B_{2}}$$

$$\Rightarrow \frac{B_{1}}{B_{2}} = \frac{9}{25}$$

$$\therefore$$   $$B_{1}:B_{2} = 9:25$$