Final answer:
The dimensions of the square framer needed to achieve an area twice that of the canvas would have a side length of the square root of 2, or approximately 1.414 meters. However, none of the provided multiple-choice options corresponds to this answer.
Step-by-step explanation:
To find the dimensions of the square framer that will result in an area twice the size of the student's 1-m square canvas, we need to calculate the area of the canvas and then determine what square dimensions would yield an area that is double the canvas's area. The area of the 1-m square canvas is 1 square meter (since area is given by the side length squared, and in this case, it's 1m x 1m). To have a framed artwork with twice the area, we would thus need a total area of 2 square meters.
To calculate the dimensions of the square framer, we look for a side length that when squared, gives us 2 square meters. We apply the square root to 2 to find the side length. The side length of the framer that will give us an area of 2 square meters is the square root of 2, which is approximately 1.414 meters. However, this side length does not match any of the available multiple-choice options. It seems there may be an error in the provided options as none corresponds to a square with an area of 2 square meters. Therefore, based on the given options, there is no correct answer to the question as framed.