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, the ratio of areas is the square of the ratio of corresponding sides.

Answer 1

The Correct Option is B

The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides. Thus, the ratio of the sides (and thus perimeters) is the square root of the ratio of areas: \[ \frac{\text{Area of triangle 1}}{\text{Area of triangle 2}} = \left( \frac{\text{Side of triangle 1}}{\text{Side of triangle 2}} \right)^2 = \frac{9}{4}. \] Taking the square root of both sides: \[ \frac{\text{Side of triangle 1}}{\text{Side of triangle 2}} = \frac{3}{2}. \] Thus, the ratio of the perimeters is also \( \boxed{3:2} \).