Question

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

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

Answer 1

Answer: (A)

$\frac{a}{x}:\frac{b}{y}$

Let the corresponding altitudes be $h_1$ and $h_2$
Then
$\frac{1}{2}\times h_1\times x=a\Rightarrow h_1=\frac{2a}{x}$ and $\frac{1}{2}\times h_2\times y-b$
$\Rightarrow h_2=\frac{2b}{y}$
$\therefore h_1:h_2=\frac{2a}{x}:\frac{2b}{y}=\frac{a}{x}:\frac{b}{y}$