To solve the problem of determining how the area of a triangle changes when its side lengths are doubled, we can follow these steps:
1. Understand the relationship between side length and area:
- When a geometric shape such as a triangle is enlarged by scaling its sides uniformly, its area changes according to the square of the scaling factor.
2. Identify the scaling factor:
- The problem states that each side of the triangle is doubled. Thus, the scaling factor is 2.
3. Apply the scaling factor to the area:
- If the original area of the triangle is [tex]\( A \)[/tex], then the area of the enlarged triangle is calculated by multiplying [tex]\( A \)[/tex] by the square of the scaling factor. This is written mathematically as:
[tex]\[
\text{new area} = A \times (\text{scale factor})^2
\][/tex]
4. Calculate the new area:
- Given the scale factor is 2, we substitute this value into the formula:
[tex]\[
\text{new area} = A \times (2)^2 = A \times 4
\][/tex]
5. Determine the ratio of the new area to the original area:
- The new area is 4 times the original area. Therefore, if the original area is 1 unit, the new area would be 4 units.
So, when the side lengths of a triangular piece of rubber are stretched to twice their original lengths, the area of the triangle becomes 4 times the original area.
Thus, the correct answer is:
"The area of the triangle increases to 4 times the original area."
