Final answer:
The ratio of the perimeter of Triangle A to Triangle B, after Triangle A is dilated by a scale factor of 2, is 1:2. This means for every unit of perimeter in Triangle A, Triangle B will have 2 units, effectively doubling the perimeter of Triangle A.
Step-by-step explanation:
If Triangle A is dilated by a scale factor of 2, then every dimension of Triangle A is doubled, including the perimeter. Therefore, if we denote the perimeter of Triangle A as P, then the perimeter of Triangle B will be 2P, assuming Triangle B is the result of the dilation.
The ratio of the perimeter of Triangle A to the perimeter of Triangle B is P to 2P, which simplifies to 1 to 2 or 1:2. This means that for every 1 unit of perimeter in Triangle A, there are 2 units of perimeter in Triangle B.
When working with the concept of scale factors, it's essential to recognize that the properties of the shape are multiplied by the scale factor. For example, in a given proportion such as 1:2=4:x, one can solve for x by cross-multiplying, which gives x=8.