The perimeter of the rectangle is 42 cm. What is the length and width of the rectangle if the length is 2 times the width.

Let’s denote the length of this rectangle through x, and the width of this rectangle through y.

According to the condition of the problem, the length of this rectangle is 2 times its width, therefore, the following relation holds:

x = 2 * y.

It is also known that the perimeter of this rectangle is 42 cm, therefore, the following relationship holds:

2 * (x + y) = 42.

We solve the resulting system of equations. Substituting into the second equation the value x = 2 * y from the first equation, we get:

2 * (2 * y + y) = 42;

2 * 3 * y = 42;

6 * y = 42;

y = 42/6;

y = 7 cm.

Knowing y, we find x:

x = 2 * y 2 * 7 = 14 cm.

Answer: the length of this rectangle is 14 cm, the width of this rectangle is 7 cm.