The perimeter of a rectangle is 40 cm. What is its area if its length is 3 times its width? 9 times?

If one side is 3 times larger than the other, and the sum of all sides is 40 cm:
2x + 6x = 40.

8x = 40.

x = 40: 8 = 5.

Width = 5 cm, length = 5 * 3 = 15 cm.

Since P = 2a + 2b. Let’s make an equation, denote the smallest side as x, and the one that is 9 times larger as 9x. The perimeter of the rectangle is 40 cm:
2 * 9x + 2 * x = 40. Let’s perform actions with the coefficients of the variable on the left side of the equation:

18x + 2x = 40.

20x = 40.

x = 40: 20 = 2.

Therefore, the measurements are 2 cm and 2 * 9 = 18 cm.