Answer:
The area of one rectangle is 15 cm²
Explanation:
The given parameters are;
The area of the square = 64 cm²
The length of the rectangles = 5 cm
The formula for the area of a square = (Side length)² = S²
Therefore, whereby the side length of the given square = S, we have;
Area of the square = 64 = S × S = S²
S = √(64 cm²) = 8 cm
The side length of the square = 8 cm
The perimeter of a square = The length of the string = Side length × 4 = 8 cm × 4 = 32 cm
∴ The perimeter of a square = The length of the string = 32 cm
The length of the string = The perimeter of the two congruent rectangle = 32 cm
Therefore;
The perimeter of each rectangle = 32/2 cm = 16 cm
Given that the length, L of the side of each rectangle is L = 5 cm, we have;
The perimeter of a rectangle = 2 × L + 2 × W
Where;
W = The width
The perimeter of the rectangle = 16 = 2 × 5 + 2 × W
2 × W = 16 - 2 × 5 = 6
W = 6/2 = 3
W = 3 cm
The width, W, of each rectangle is W = 3 cm
The area of one rectangle = W × L = 3 cm × 5 cm = 15 cm²
The area of one rectangle = 15 cm².