Question

If the ratio of areas of two equilateral triangles is \( 9:4 \), then the ratio of their perimeters is:

• A. \( 27:8 \)
• B. \( 3:2 \)
• C. \( 9:4 \)
• D. \( 4:9 \)

Hint:

For similar triangles: \[ \text{Ratio of Perimeters} = \sqrt{\text{Ratio of Areas}}. \]

Answer 1

The Correct Option is B

For similar triangles, the ratio of their areas is the square of the ratio of their sides.
\[ \left(\frac{\text{Perimeter}_1}{\text{Perimeter}_2}\right)^2 = \frac{\text{Area}_1}{\text{Area}_2}. \] \[ \left(\frac{P_1}{P_2}\right)^2 = \frac{9}{4}. \] \[ \frac{P_1}{P_2} = \frac{3}{2}. \] Thus, the ratio of their perimeters is \( 3:2 \).