The length of each side of an equilateral triangle will be doubled to create a second triangle. The area of the second triangle will be how many times the area of the original triangle?

Answer

To solve the problem, we need to find the area of both the original equilateral triangle and the new triangle formed by doubling the side lengths.

### Step 1: Area of the Original Triangle
The formula for the area \( A \) of an equilateral triangle with side length \( a \) is given by:

\[ A = \frac{\sqrt{3}}{4} a^2 \]

For the original triangle (Triangle 1), the side length is \( A \).

\[ A_1 = \frac{\sqrt{3}}{4} A^2 \]

### Step 2: Area of the New Triangle
Now, for the new triangle (Triangle 2), the side length is doubled, so the new side length is \( 2A \). We will use the same area formula for the new triangle:

\[ A_2 = \frac{\sqrt{3}}{4} (2A)^2 \]

Calculating \( (2A)^2 \):

\[ (2A)^2 = 4A^2 \]

Now substituting this back into the area formula:

\[ A_2 = \frac{\sqrt{3}}{4} \cdot 4A^2 \]

This simplifies to:

\[ A_2 = \sqrt{3} A^2 \]

### Step 3: Finding the Ratio of the Areas
Now, we need to find how many times the area of the second triangle is compared to the first triangle. We will calculate the ratio \( \frac{A_2}{A_1} \):

\[ \frac{A_2}{A_1} = \frac{\sqrt{3} A^2}{\frac{\sqrt{3}}{4} A^2} \]

The \( A^2 \) terms cancel out:

\[ \frac{A_2}{A_1} = \frac{\sqrt{3}}{\frac{\sqrt{3}}{4}} = \frac{\sqrt{3} \cdot 4}{\sqrt{3}} = 4 \]

### Conclusion
The area of the second triangle (Triangle 2) is 4 times the area of the original triangle (Triangle 1).

### Final Answer
The area of the second triangle will be **4 times** the area of the original triangle.