Question

If an equilateral triangle \( \triangle ABC \) has one side of 12 cm, and another equilateral triangle \( \triangle DEF \) has one side of 6 cm, then what is the ratio of their areas?

• A. \( 2:1 \)
• B. \( 1:2 \)
• C. \( 4:1 \)
• D. \( 2:3 \)

Hint:

For similar triangles, the ratio of their areas is given by: \[ \text{Area Ratio} = \left(\frac{\text{Side}_1}{\text{Side}_2}\right)^2 \]

Answer 1

The Correct Option is C

For similar triangles, the ratio of their areas is the square of the ratio of their corresponding sides.
Given the side ratio:
\[ \frac{AB}{DE} = \frac{12}{6} = 2:1 \] The ratio of areas is:
\[ \left(\frac{12}{6}\right)^2 = 4:1 \]