The perimeter of the rectangle is 100 cm. What is the length and width of the rectangle if the length is 4 times the width?

Let’s denote by x the width of this rectangle. According to the condition of the problem, the length of this rectangle is 4 times the width of this rectangle, therefore, the length of this rectangle is 4 * x. It is also known that the perimeter of this rectangle is 100 cm, therefore, we can make the following equation: 2 * (x + 4 * x) = 100. Solve the resulting equation and find the width of this rectangle: 2 * 5 * x = 100; 10 * x = 100; x = 100/10; x = 10 cm. Knowing the width of this rectangle, we find its length: 4 * x = 4 * 10 = 40 cm.
Answer: the width of the rectangle is 10 cm, the length of the rectangle is 40 cm.