Question

In similar triangles, the ratio of corresponding altitudes is 2:5. What is the ratio of their areas?

• A. 2 : 5
• B. 4 : 25
• C. 2 : 25
• D. 5 : 2

Answer 1

Answer:

B. 4 : 25

In similar triangles, all corresponding linear dimensions (sides, heights, medians, altitudes, etc.) are in the same ratio.

Given:

$\text{Ratio of altitudes} = 2:5$

The ratio of areas of similar triangles is the square of the ratio of corresponding sides (or altitudes):

$\text{Area ratio} = \left(\frac{2}{5}\right)^2$

$= \frac{4}{25}$

Answer:

$\boxed{4:25}$