Question:
In \( \triangle ABC \) and \( \triangle PQR \), the area of \( \triangle ABC \) is to the area of \( \triangle PQR \) as \( 49:16 \), then the ratio of their corresponding sides is:
In \( \triangle ABC \) and \( \triangle PQR \), the area of \( \triangle ABC \) is to the area of \( \triangle PQR \) as \( 49:16 \), then the ratio of their corresponding sides is:
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The ratio of areas of similar triangles is the square of the ratio of their corresponding sides.
Updated On: Oct 27, 2025
- 49:16
- 25:16
- 36:49
- 81:64
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The Correct Option is A
Solution and Explanation
The ratio of areas of two similar triangles is the square of the ratio of their corresponding sides. Therefore, the ratio of the sides is the square root of the ratio of areas:
\[
\frac{\text{Area of } \triangle ABC}{\text{Area of } \triangle PQR} = \frac{49}{16}.
\]
Taking the square root of both sides:
\[
\frac{\text{Side of } \triangle ABC}{\text{Side of } \triangle PQR} = \frac{7}{4}.
\]
Thus, the correct answer is \( \boxed{49:16} \).
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