Question

Heights of two similar triangles are 3 cm and 4 cm respectively. Ratio of the areas of the triangles will be:

• A. 9 : 16
• B. 27 : 16
• C. 16 : 81
• D. 4 : 9

Hint:

The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides.

Answer 1

The Correct Option is A

For similar triangles, the ratio of their areas is the square of the ratio of their corresponding sides (including heights). Given the heights of two similar triangles are 3 cm and 4 cm, the ratio of the areas of the triangles will be: \[ \text{Ratio of areas} = \left(\frac{3}{4}\right)^2 = \frac{9}{16} \]
Step 2: Conclusion.
Thus, the ratio of the areas is $9 : 16$. So, the correct answer is (A).