Question

If one side of an equilateral triangle \( ABC \) is 12 cm and one side of equilateral triangle \( DEF \) is 6 cm, then the ratio of areas of \( \frac{\triangle ABC}{\triangle DEF} \) is:

• A. 2:1
• B. 1:2
• C. 4:1
• D. 2:3

Hint:

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

Answer 1

The Correct Option is C

Step 1: The area of an equilateral triangle is proportional to the square of the side length. If the side lengths are in the ratio \( 12:6 = 2:1 \), then the ratio of their areas is \( (2^2):(1^2) = 4:1 \). Thus, the correct answer is \( 4:1 \).