A rectangle with sides of 4 cm and 8 cm was cut into 4 identical rectangles. What is the perimeter of one rectangle?

This problem has two solutions. They differ from each other in how they divide the large rectangle into four small ones.

Divide the rectangle into parts relative to its long side
So, we have a rectangle with sides equal to 4cm and 8cm. Before dividing this rectangle into four small ones, we need to think about how we will do it.

In the first variant of solving the problem, we divide the rectangle parallel to its short side. That is, we divide the 8 cm side into four parts.

Let’s take one of the new rectangles. We got that one side of it coincides with the length of the short side of the large rectangle and is equal to 4 cm. And the second side is equal to 1/4 of the length of the larger side of the large rectangle. Let’s move on to the calculations:

8/4 = 2 (cm) – the length of the second side of the new rectangle;
2 + 2 + 4 + 4 = 12 (cm) – the perimeter of the new rectangle (the perimeter is equal to the sum of the lengths of all sides); or:
2 * 2 + 4 * 2 = 4 + 8 = 12 (cm) – the second option for finding the perimeter.
So the answer is: the perimeter of one of the new rectangles is 12 cm.

Divide the rectangle into parts relative to its short side
In the second variant of solving the problem, we divide the rectangle parallel to its long side. That is, we divide the 4 cm side into four parts.

Let’s take one of the new rectangles. We got that one side of it coincides with the length of the larger side of the large rectangle and is equal to 8 cm. And the second side is equal to 1/4 of the length of the short side of the large rectangle. Let’s move on to the calculations:

4/4 = 1 (cm) – the length of the second side of the new rectangle;
1 + 1 + 8 + 8 = 18 (cm) – the perimeter of the new rectangle; or:
1 * 2 + 8 * 2 = 2 + 16 = 18 (cm) – the second option for finding the perimeter.
Answer: The perimeter of one of the new rectangles is 18 cm.