The area of the square is 64 cm². Find the perimeter of this square. Which sides can have a rectangle

| April 14, 2021 | education

The area of the square is 64 cm². Find the perimeter of this square. Which sides can have a rectangle with the same perimeter, if they are expressed as an integer number of centimeters. Find the areas of such rectangles.

1. According to the problem statement, the area of the square is S = 64 cm².

Since the area is equal to the square of the side, then the side a = 8 cm.

2. The perimeter is equal to the sum of the four sides.

P = 4 * 8 = 32 cm.

3. The perimeter of the rectangle is twice the sum of the length and width.

So the sum of the length and width is 32/2 = 16 cm.

Possible rectangles with parameters:

1 and 15, area 1 * 15 = 15 cm².

2 and 14, area 2 * 14 = 28 cm².

3 and 13, area 3 * 13 = 39 cm².

4 and 12, area 4 * 12 = 48 cm².

5 and 11, area 5 * 11 = 55 cm².

6 and 10, area 6 * 10 = 60 cm².

7 and 9, area 7 * 9 = 63 cm².

Answer: perimeter 32 cm; 7 different rectangles.



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