Final answer:
To find the perimeter of the larger rectangle, we consider the combined length of the three smaller rectangles (18 cm) and the height of the fourth rectangle (6 cm). The perimeter of the larger rectangle is 48 cm regardless of whether the fourth rectangle is placed adjacent to or on top of the three smaller rectangles.
Step-by-step explanation:
To calculate the perimeter of the larger rectangle formed by three smaller rectangles each measuring 3 cm by 6 cm and an additional rectangle that is 6 cm tall, we first need to determine the dimensions of the larger rectangle. If the three smaller rectangles are placed side by side, their combined length will be 18 cm (as 3 times 6 cm equals 18 cm), and the height will remain the same at 3 cm because they are placed horizontally.
For the fourth rectangle, which is 6 cm tall, it is not clearly stated whether its length is the same as the smaller rectangles or different.
Assuming it has the same length of 6 cm, it can be placed either adjacent to the three rectangles or on top of them to form a square. Either way, the height of the larger rectangle will increase by 6 cm, making the final height either 9 cm or 6 cm.
Assuming the fourth rectangle is placed on top of the three to make a square, the dimensions of the larger rectangle are now 6 cm by 6 cm. Therefore, the perimeter is 4(length) + 4(height) = 4(6 cm) + 4(6 cm) = 48 cm.
If instead, we place the fourth rectangle adjacent, the larger rectangle would measure 6 cm by 9 cm, and the perimeter would be 2(length) + 2(height) = 2(18 cm) + 2(6 cm) = 48 cm. In both cases, the perimeter of the larger rectangle is 48 cm.