Question

Investigate the area of rectangles with the same perimeter but which do not share that perimeter with a square (18 cm, 22cm,26cm, etc ). Do you find the same relationship between length of rectangle and size of area? Is there a pattern in the areas of the rectangles? Describe it.

Answer 1

There is a pattern in the areas of rectangles with the same perimeter. The larger the length of the rectangle, the larger the area.

Step-by-step explanation:

When investigating the area of rectangles with the same perimeter, we can find a relationship between the length of the rectangle and the size of the area.

Let's consider two rectangles with the same perimeter of 18 cm. The first rectangle has a length of 9 cm and a width of 0.5 cm, giving it an area of 4.5 cm². The second rectangle has a length of 4.5 cm and a width of 2.5 cm, giving it an area of 11.25 cm². Comparing these two rectangles, we can see that as the length of the rectangle increases, the area also increases.

Therefore, there is a pattern in the areas of the rectangles with the same perimeter: the larger the length of the rectangle, the larger the area.