The area of a rectangle is 100 square centimeters. If the length is reduced by four times and the width is increased by four times, the rectangle will become a square, and the area of the square

The area of a rectangle is 100 square centimeters. If the length is reduced by four times and the width is increased by four times, the rectangle will become a square, and the area of the square

Let the original length be a and the width be B
Then a * b = 100
（1/4）a=4b
The solution is a = 40
b=2.5
Then the side length of the square is 4B = 10
Square area = 10 * 10 = 100 square centimeter
I said it's complicated
Let the original length a, width B
ab=100
After becoming a square, the area s = (1 / 4) a * 4B = AB = 100