Question

If \( \triangle ABC \sim \triangle DEF \) and \( \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} = \frac{5}{7} \), 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:

For similar triangles: \[ \text{Ratio of Areas} = \left(\text{Ratio of Corresponding Sides}\right)^2. \]

Answer 1

The Correct Option is B

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides.
\[ \text{Ratio of Areas} = \left(\frac{\text{Side}_1}{\text{Side}_2}\right)^2. \] \[ \left(\frac{5}{7}\right)^2 = \frac{25}{49}. \]