The perimeter of the rectangle is 80cm. What should be its length and width so that the area

The perimeter of the rectangle is 80cm. What should be its length and width so that the area of the rectangle is the largest?

Let’s write down the formulas for the perimeter and area of the rectangle and consider the possible options for the length and width.
P = 2 * (a + b), S = a * b.
2 * (a + b) = 80
a + b = 40.
a = 1, b = 39, S = 1 * 39 = 39;
a = 2, b = 38, S = 2 * 38 = 76;
a = 3, b = 37, S = 3 * 36 = 108;
a = 4, b = 35, S = 4 * 35 = 140.
So you can go on and get to:
a = 20, b = 20, S = 20 * 20 = 400. This will be the maximum area, and the rectangle is a square with a side of 20 cm.