Question

In \( \triangle ABC \) and \( \triangle DEF \), \( \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} = \frac{5}{7} \), then the ratio of the areas of \( \triangle ABC \) and \( \triangle DEF \) is:

• A. 5:7
• B. 25:49
• C. 49:25
• D. 125:343

Hint:

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

Answer 1

The Correct Option is B

For two similar triangles, the ratio of their areas is the square of the ratio of their corresponding sides. Since \( \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} = \frac{5}{7} \), the ratio of the areas is: \[ \frac{\text{Area of } \triangle ABC}{\text{Area of } \triangle DEF} = \left( \frac{5}{7} \right)^2 = \frac{25}{49}. \] Thus, the correct answer is \( \boxed{25:49} \).