Question

The areas of two similar triangles are in the ratio 81:121. The ratio of their sides will be:

• A. 9:11
• B. 11:9
• C. 3:19
• D. 19:3

Hint:

In similar triangles, the ratio of the areas is equal to the square of the ratio of their corresponding sides.

Answer 1

The Correct Option is A

Step 1: Understanding the relation between areas and sides of similar triangles.
The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides. \[ \text{Ratio of areas} = (\text{Ratio of sides})^2 \]
Step 2: Applying the given ratio of areas.
We are given the ratio of areas as \( 81:121 \). Therefore: \[ \left(\frac{\text{side 1}}{\text{side 2}}\right)^2 = \frac{81}{121} \]
Step 3: Taking the square root of both sides.
\[ \frac{\text{side 1}}{\text{side 2}} = \sqrt{\frac{81}{121}} = \frac{9}{11} \] Thus, the ratio of the sides is \( 9:11 \). The correct answer is (A).