Final answer:
When you double the lengths of a rectangle, the new area is four times its original size. This is because both the length and width are doubled, and area is calculated by multiplying length by width.
Step-by-step explanation:
If you double the lengths of a rectangle, each dimension of the rectangle (length and width) would be twice as long. Since the area of a rectangle is calculated by multiplying the length by the width, when both dimensions are doubled, the new area is four times its original size. Therefore, if the original rectangle had an area of 'A', after doubling the lengths, the new area would be '4A'. This concept is similar to scaling in geometry where a scale factor of 2 applied to both dimensions results in an area that is 22, or 4 times greater.
For example, if we have two rectangles and the second rectangle has dimensions that are twice that of the first rectangle, then the second rectangle's area is four times the first one. If the first rectangle has dimensions L and W, its area is L x W. If the second rectangle has dimensions 2L and 2W, its area is 2L x 2W, which simplifies to 4 x (L x W), hence four times the original area.
So, the correct answer to the question is C: The area of the new rectangle is four times its original size.