Question

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:

• A. $ax:by$
• B. $\frac{a}{x}:\frac{b}{y}$
• C. $ay:bx$
• D. $\frac{x}{a}:\frac{b}{y}$

Answer 1

The correct option is C $ay:bx$

Let their altitudes be $l_1$ & $l_2$

ratio of areas $=\frac{a}{b}=\frac{\frac{1}{2}{l}_{1}x}{\frac{1}{2}{l}_{2}y}$

$\frac{a}{b}=\frac{l_{1}x}{l_{2}y}$

$\frac{l_1}{l_2}=\frac{a_y}{b_x}$