Question

If ratio of sides of two similar triangles is 4:7, then ratio of their areas will be:

• A. 4:7
• B. 16:49
• C. 49:16
• D. 64:243

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 B

We are given that the ratio of the sides of two similar triangles is \( 4:7 \). To find the ratio of their areas, we use the property that the ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides.
Step 1: Apply the property of areas of similar triangles.
The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides: \[ \frac{\text{Area}_1}{\text{Area}_2} = \left( \frac{\text{Side}_1}{\text{Side}_2} \right)^2 \] Given that the ratio of the sides is \( \frac{4}{7} \), the ratio of the areas will be: \[ \frac{\text{Area}_1}{\text{Area}_2} = \left( \frac{4}{7} \right)^2 = \frac{16}{49} \]
Step 2: Conclusion.
Thus, the ratio of the areas of the two triangles is \( 16:49 \). The correct answer is (B).