Final answer:
To find the width of the rectangle, we need to calculate the area of the square by dividing its perimeter by 4 and then squaring the result. The measured width of the rectangle is 1.25 cm, but using the correct calculations, the width should be 1 cm (option b) to match the square's area of 0.25 cm².
Step-by-step explanation:
The question asks us to find the width of a rectangle when one of its dimensions (length) is given in terms of the area of a square with a known perimeter. First, to find the side length of the square, we divide the perimeter by 4 (since each of the four sides of a square is equal), which yields 2 cm / 4 = 0.5 cm as the side length of the square. Then, the area of the square (which equals the length of the rectangle) is the square of the side length, hence 0.5 cm × 0.5 cm = 0.25 cm².
Given the measured width of the rectangle is 1.25 cm, we can confirm that this measurement would make the rectangle's area 1.25 cm × 0.5 cm (width × length), which is not equal to 0.25 cm², and hence an incorrect width. Based on the choices provided and the clue that the width is more than 1.0 cm but less than 2.0 cm, the width is too large to be option a) 0.5 cm and option b) 1 cm. Since we know the length of the rectangle is the area of the square, which is 0.25 cm², and the width must produce this area, the correct width of the rectangle would be 1 cm (option b).
Therefore, the answer must be option b) 1 cm, as it is the only width that will result in a rectangle with an area equal to 0.25 cm² when multiplied by the given length. We do not choose c) 2 cm or d) 4 cm because they would give us a much larger area than 0.25 cm² when multiplied by 1 as a length.