For a square with side length ACM (a > 2), if one side is increased by 2cm and the other side is decreased by 2cm, which is the larger area of the changed figure than that of the original square? How much bigger?

For a square with side length ACM (a > 2), if one side is increased by 2cm and the other side is decreased by 2cm, which is the larger area of the changed figure than that of the original square? How much bigger?

The area before the change = A2; the area after the change is: (a + 2) (A-2) = A2-4, the area of the changed figure is smaller than that of the original square, a2 - (A2-4) = 4

For a square with side length of ACM (a > 2), if one of the two adjacent sides increases by 2cm and the other decreases by 2cm, then ()
A. Perimeter and area remain unchanged B. perimeter remains unchanged, area becomes smaller C. area remains unchanged, perimeter becomes larger D. area remains unchanged, perimeter becomes smaller

Let the side length of the original square be a, then the length of the changed figure is (a + 2), the width is (A-2), the perimeter of the original square is a × 4 = 4A (CM), the perimeter of the new rectangle is (a + 2 + A-2) × 2 = 4A (CM); the area of the square is a × a = A2 (CM), the area of the rectangle is (a + 2) × (A-2) = A2-4 (CM); therefore, the perimeter remains unchanged, and the area decreases Less 4 square centimeters. So the answer is: B

Why is the area of a rectangle = length by width, and why is the area of a square = side length by side length?

The standard stipulates that the area of a small square of 1 square centimeter is 1 square centimeter
The area of a rectangle is the sum of the areas of all small squares. The area of all small squares is the sum of the areas of all small squares: the number of small squares in each row multiplied by the number of queues, and the number of small squares in each row is exactly the number of centimeters contained in the long side, So the number of rows is exactly the number of centimeters contained in the wide side. So the area of a rectangle is equal to the length times the width
Square is a special rectangle, which is also derived by the above methods

A rectangular piece of paper is 36cm long and 30cm wide. If you want to cut this piece of paper into a small square with equal area and no surplus, what is the maximum side length of the square?
A rectangular piece of paper is 36cm long and 30cm wide. If you want to cut this piece of paper into a small square with equal area and no surplus, what is the maximum side length of the square?

This is the greatest common divisor of 36 and 30, so the side length is 6cm