The areas of two equilateral triangles are in the ratio 25 : 36. Their altitudes will be in the ratio

### Concept & Formula The area of similar figures is proportional to the square of their corresponding linear dimensions (sides, altitudes, medians). $$ \frac{A_1}{A_2} = \left(\frac{h_1}{h_2}\right)^2 $$ ### Step-by-Step Solution 1. We are given the ratio of the areas of two equilateral triangles: $\frac{A_1}{A_2} = \frac{25}{36}$. 2. The ratio of their altitudes $h_1$ and $h_2$ is the square root of the ratio of their areas. 3. $\frac{h_1}{h_2} = \sqrt{\frac{A_1}{A_2}} = \sqrt{\frac{25}{36}}$. 4. $\frac{h_1}{h_2} = \frac{5}{6}$. ### Exam Strategy & Shortcut For any 2D similar shapes (including all equilateral triangles), Area Ratio = (Side Ratio)$^2$ = (Altitude Ratio)$^2$. Simply take the square root of 25:36 to get 5:6. ### Common Pitfall Assuming altitude ratio is the same as area ratio, or squaring the area ratio instead of taking the square root. ### Final Answer Therefore, the correct answer is **5 : 6**.