Final answer:
The change in area is 0 cm² and the change in perimeter is -400cm.
Step-by-step explanation:
To find the change in area and perimeter of the bed sheets, we need to first calculate the area and perimeter of the single bed sheets and the double bed sheet.
The dimensions of the double bed sheet are 160cm × 200cm. Since John stitched together two equal-sized single bed sheets to make the double bed sheet, each single bed sheet would have dimensions of 160cm/2 = 80cm × 200cm
The area of each single bed sheet is calculated by multiplying the length and width: 80cm × 200cm = 16,000 cm². The perimeter is calculated by adding twice the length and twice the width: 2(80cm + 200cm) = 2 × 280cm = 560cm.
The area of the double bed sheet is calculated by multiplying the length and width: 160cm × 200cm = 32,000 cm². The perimeter is calculated by adding twice the length and twice the width: 2(160cm + 200cm) = 2 × 360cm = 720cm.
The change in area is given by the difference between the area of the double bed sheet and the area of two single bed sheets: 32,000 cm² - 2(16,000 cm²) = 32,000 cm² - 32,000 cm² = 0 cm².
The change in perimeter is given by the difference between the perimeter of the double bed sheet and the perimeter of two single bed sheets: 720cm - 2(560cm) = 720cm - 1120cm = -400cm.