Final answer:
When the length and width of a rectangle are both doubled, the area of the rectangle is quadrupled. For a rectangle with original dimensions of 4.5 inches by 3 inches, the new dimensions would be 9 inches by 6 inches, resulting in an area that is four times larger than the original.
Step-by-step explanation:
A student asked how the area would change if the dimensions of a rectangle were doubled. The original rectangle has a length of 4.5 inches and a width of 3 inches.
To find the area of the new, larger rectangle after doubling both the length and the width, we apply the scale factor of 2. The new length would be 4.5 inches × 2 = 9 inches, and the new width would be 3 inches × 2 = 6 inches. The area of the original rectangle is length × width, which is 4.5 inches × 3 inches = 13.5 square inches. For the new rectangle, the area is also length × width, which is 9 inches × 6 inches = 54 square inches.
When comparing the two areas, we find that the area of the larger rectangle is four times the area of the original rectangle (54 square inches is 4 times 13.5 square inches). This demonstrates that when the dimensions of a figure are doubled, the area increases by a factor of the scale factor squared, which in this case is 2² = 4. Therefore, the new area is four times larger than the original area.