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:

• A. 49:16
• B. 25:16
• C. 36:49
• D. 81:64

Hint:

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

Answer 1

The Correct Option is A

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 \( \boxed{49:16} \).