Let's solve the problem step-by-step.
1. Determine the dimensions of the original paper:
- The area of the original rectangular piece of hand-made paper is given as 120 square inches.
- Since the problem doesn't specify the length and width, we can assume for simplicity that the paper is square. The side length of a square with an area of 120 square inches is calculated by taking the square root of 120.
- Therefore, the side length of the original paper is [tex]\( \sqrt{120} \)[/tex].
2. Calculate the dimensions of the foil:
- The problem states that Martha needs the foil to be of exactly double the dimensions of the original paper.
- If the side length of the original paper is [tex]\( \sqrt{120} \)[/tex], then doubling the dimensions means the new side length will be [tex]\( 2 \times \sqrt{120} \)[/tex].
3. Calculate the area of the foil:
- The area of a square is given by the side length squared.
- Therefore, the area of the foil with the doubled side length will be [tex]\( (2 \times \sqrt{120})^2 \)[/tex].
4. Simplify the calculation:
- Let’s break this down:
[tex]\[
(2 \times \sqrt{120})^2 = 4 \times 120 = 480
\][/tex]
Thus, the area of the foil that Martha needs is [tex]\( 480 \)[/tex] square inches.
The correct answer is:
B) [tex]\( 480 \)[/tex] in[tex]\( ^2 \)[/tex]
