Beatrice is a designer. She wants to reproduce one of her designs on an A1 sheet from an A3 sheet. What do you think should be the scaling factor for this magnification?
A. (141 percent)
B. (282 percent)
C. (100 percent)
D. (200 percent)
To determine the scaling factor for magnifying a design from an A3 sheet to an A1 sheet, we can use the aspect ratio of the two paper sizes.
The aspect ratio is the ratio of the longer side to the shorter side of a sheet of paper. The aspect ratio of an A3 sheet is 1:√2, while the aspect ratio of an A1 sheet is 1:2.
To calculate the scaling factor, we need to compare the aspect ratios of the two paper sizes. We can do this by dividing the longer side of the A1 sheet by the longer side of the A3 sheet:
Scaling factor = (longer side of A1 sheet) / (longer side of A3 sheet)
= 2 / (1 x √2)
= 2 / √2
= √2
The resulted scaling factor is √2, which is approximately 1.41.
Therefore, the scaling factor for this enlargement should be approximately 141 percent, which corresponds to option A.