Question

If the corresponding sides of two similar triangles are in the ratio 3:5, the ratio of their areas will be:

• A. 9:25
• B. 6:10
• C. 3:5
• D. 25:9

Hint:

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

Answer 1

The Correct Option is A

We are given that the corresponding sides of two similar triangles are in the ratio 3:5. To find the ratio of their areas, we use the property that the ratio of the areas of two similar figures is the square of the ratio of their corresponding sides.
Step 1: Use the property of areas of similar figures.
The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides. Given: \[ \text{Ratio of sides} = \frac{3}{5} \] The ratio of the areas will be: \[ \text{Ratio of areas} = \left( \frac{3}{5} \right)^2 = \frac{9}{25} \]
Step 2: Conclusion.
Therefore, the ratio of the areas of the two similar triangles is 9:25. The correct answer is (A).