The ratio of bases of two triangles is x : y and that of their areas is a : b. Then the ratio of their corresponding altitudes will be :

$$\eqalign{ & \frac{a}{b} = \frac{{\frac{1}{2}x \times {h_1}}}{{\frac{1}{2}y \times {h_2}}}bx{h_1} = ay{h_2} \cr & \Leftrightarrow \frac{{{h_1}}}{{{h_2}}} = \frac{{ay}}{{bx}} \cr} $$
\[\left[ \begin{gathered} {\text{Ratio of areas}} = \frac{a}{b}{\text{ }} \hfill \\ {\text{Ratio of base}} = x:y \hfill \\ \end{gathered} \right]\]

$${\text{Hence, }}{h_1}:{h_2} = ay:bx$$