4

Step 1: Determine the Side Lengths
Let the side length of the first equilateral triangle be \( a \) and the second triangle be \( 2a \).

Step 2: Calculate the Moment of Inertia
The moment of inertia of an equilateral triangle about one of its sides is given by the formula:
\[ I = \frac{1}{3} \times \text{base} \times \text{height}^3 \text{ (for side as base)} \]
For the first triangle, the height \( h_1 \) is given by:
\[ h_1 = \frac{\sqrt{3}}{2} a \]
Thus moment of inertia \( I_1 \) is
\[ I_1 = \frac{1}{3} \times a \times \left(\frac{\sqrt{3}}{2}a\right)^3 = \frac{1}{3} \times a \times \frac{3\sqrt{3}}{8} a^3 = \frac{\sqrt{3}}{8} a^4 \]

For the second triangle (side length = 2a), the height \( h_2 \) is:
\[ h_2 = \frac{\sqrt{3}}{2} \cdot 2a = \sqrt{3} a \]
Thus, moment of inertia \( I_2 \) is
\[ I_2 = \frac{1}{3} \times 2a \times (\sqrt{3} a)^3 = \frac{1}{3} \times 2a \times 3\sqrt{3}a^3 = 2\sqrt{3} a^4 \]

Step 3: Calculate the Ratio of Moments of Inertia
The ratio \( \frac{I_2}{I_1} \) is:
\[ \frac{I_2}{I_1} = \frac{2\sqrt{3}a^4}{\frac{\sqrt{3}}{8} a^4} = 2 \times 8 = 16 \]

Final Result
The ratio of the moments of inertia \( \frac{I_2}{I_1} \) is equal to 16.