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:
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:
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For similar triangles:
\[
\text{Ratio of Areas} = \left(\text{Ratio of Corresponding Sides}\right)^2.
\]
Updated On: Oct 27, 2025
- \( 5:7 \)
- \( 25:49 \)
- \( 49:25 \)
- \( 125:343 \)
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The Correct Option is B
Solution and Explanation
The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides.
\[ \text{Ratio of Areas} = \left(\frac{\text{Side}_1}{\text{Side}_2}\right)^2. \] \[ \left(\frac{5}{7}\right)^2 = \frac{25}{49}. \]
\[ \text{Ratio of Areas} = \left(\frac{\text{Side}_1}{\text{Side}_2}\right)^2. \] \[ \left(\frac{5}{7}\right)^2 = \frac{25}{49}. \]
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