Final answer:
The side length of square R is 1 inch, and the rectangles have a perimeter of 7 inches. The side length of square T is 7 inches, leading to a perimeter of 28 inches. The concept of a scale factor is applied to determine size changes and related perimeters.
Step-by-step explanation:
Finding the Perimeter of Square T
To solve the question, we must first determine the side length of square R, which has an area of 1 square inch. Since area equals side length squared, the side length of square R is 1 inch. The perimeter of each of the rectangles is 7 inches; if we call the longer side of the rectangle 'l' and the shorter side 'w', then 2l + 2w = 7 inches. We know that w must be equal to 1 inch because it is the same as the side of square R. Therefore, solving 2l + 2(1) = 7 inches gives us l = 3 inches.
Knowing that square R and the two rectangles form part of the larger square T, we understand that the side of square T must be twice the side of rectangle R plus the side of square R, which equates to 2 * 3 inches + 1 inch = 7 inches. Therefore, the perimeter of square T is 4 times its side length, which is 4 * 7 inches = 28 inches.
The scale factor concept helps to understand that when the dimensions of a figure are scaled by a certain factor, the perimeter of the figure will also be multiplied by the same factor.