four congruent rectangles are arranged as shown to form an inner square of area 20 cm2 and an outer square of area 64 cm2 . what is the perimeter of one of the four congruent rectangles?

To solve this problem, we first need to understand the relationship between the inner square, the outer square, and the four congruent rectangles.

Step 1: Find the side length of the inner square. The area of a square is found by squaring one of its sides. So, if the area of the inner square is 20 cm², its side length is the square root of 20, which is approximately 4.47 cm.

Step 2: Find the side length of the outer square. Similarly, if the area of the outer square is 64 cm², its side length is the square root of 64, which is 8 cm.

Step 3: Find the dimensions of the rectangles. The rectangles are arranged such that the length of each rectangle is equal to the side length of the outer square, and the width of each rectangle is the difference between the side length of the outer square and the side length of the inner square. So, the length of each rectangle is 8 cm, and the width is 8 cm - 4.47 cm = 3.53 cm.

Step 4: Find the perimeter of one rectangle. The perimeter of a rectangle is found by adding up all its sides, or 2 times the length plus 2 times the width. So, the perimeter of one rectangle is 2 * 8 cm + 2 * 3.53 cm = 23.06 cm.