The ratio of bases of two triangles is x: y a | vedclass

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(C) Let the bases of the two triangles be $b_1$ and $b_2$,and their altitudes be $h_1$ and $h_2$ respectively.Given that the ratio of their bases is $

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$a y: b x$

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(C) Let the bases of the two triangles be $b_1$ and $b_2$,and their altitudes be $h_1$ and $h_2$ respectively.Given that the ratio of their bases is $\frac{b_1}{b_2} = \frac{x}{y}$ and the ratio of their areas is $\frac{\Delta_1}{\Delta_2} = \frac{a}{b}$.The area of a triangle is given by the formula $\Delta = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{altitude}$.Therefore,$\frac{\Delta_1}{\Delta_2} = \frac{\frac{1}{2} b_1 h_1}{\frac{1}{2} b_2 h_2} = \frac{b_1}{b_2} 	imes \frac{h_1}{h_2}$.Substituting the given values,we get $\frac{a}{b} = \frac{x}{y} 	imes \frac{h_1}{h_2}$.Solving for the ratio of altitudes $\frac{h_1}{h_2}$,we get $\frac{h_1}{h_2} = \frac{a}{b} 	imes \frac{y}{x} = \frac{ay}{bx}$.Thus,the ratio of their corresponding altitudes is $ay: bx$.

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

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