The area of two similar triangles is $16\ cm^{2}$ and $25\ cm^{2}$. Find the ratio of their corresponding altitudes.

Given: The area of two similar triangles is $16\ cm^{2}$ and $25\ cm^{2}$.

To do: To find the ratio of their corresponding altitudes.

Solution: 

Let the corresponding sides of the triangles be $x$ and $y$.

As known, $\frac{Area( 1st\ triangle)}{Area( 2nd\ triangle)} =$ Square of ratio of corresponding sides

$\Rightarrow \frac{16}{25}=( \frac{x}{y})^{2}$

$\Rightarrow \frac{x}{y}=\sqrt{\frac{16}{25}}$  

$\Rightarrow \frac{x}{y}=\frac{4}{5}$

$\Rightarrow x:y=4:5$

Therefore, the ratio of the corresponding altitudes is $4:5$.