Final answer:
The side length of square T is 6 inches, which is derived from the lengths of two adjacent rectangles plus the side of square R. Multiplying this by 4, the perimeter of square T is 24 inches.
Step-by-step explanation:
To find the perimeter of square T, we need to establish the side length of square T. We are given that the side length of square R is 1 inch, meaning each side of square R measures 1 inch. Since square R has an area of 1 square inch, it is a 1x1 square. Given that the perimeters of the rectangles are 7 inches, and the rectangles are identical, we can calculate their dimensions. The perimeter of a rectangle can be calculated as the sum of twice its width plus twice its length, represented by the formula P = 2l + 2w. If the width of the rectangle is 1 inch (equal to the side of the square R since they assemble to form a larger square), we have 7 = 2l + 2(1). Solving for l, we get 7 = 2l + 2, which simplifies to 5 = 2l, and hence l = 2.5 inches. Therefore, the length of the rectangle is 2.5 inches.
Now, to find the dimensions of the larger square T, we need to consider that square T consists of two lengths of the rectangles plus one side of square R. Thus, the side of square T measures 2l + 1. Substituting the length we found for the rectangle, this gives us 2(2.5) + 1, which equals 5 + 1, and so the side of square T measures 6 inches. Finally, since the perimeter is the sum of all sides, and a square has four equal sides, the perimeter of square T is 4 times the side length, or 4(6), which equals 24 inches.