Final answer:
The percentage of change in the area of a rectangle with initial dimensions 6 inches by 4 inches, after doubling the dimensions, is 300%. The percentage of change in the perimeter after doubling the dimensions is 100%.
Step-by-step explanation:
Let's find the percentage of change in the area and the percentage of the perimeter for a rectangle with dimensions 6 inches by 4 inches. First, we calculate the original area and perimeter, then we'll calculate the new area and perimeter if dimensions are doubled, and finally, we'll find the percentage change.
The original area is 6 inches × 4 inches = 24 square inches. If both dimensions are doubled, the new dimensions are 12 inches × 8 inches, so the new area is 96 square inches. The percentage change in area is ((new area - original area) / original area) × 100%, which is ((96 - 24) / 24) × 100% = 300%.
The original perimeter is 2 × (6 inches + 4 inches) = 20 inches. After doubling the dimensions, the new perimeter is 2 × (12 inches + 8 inches) = 40 inches. The percentage of change in the perimeter is
((new perimeter - original perimeter) / original perimeter) × 100%, which is ((40 - 20) / 20) × 100% = 100%.