The perimeter of the rectangle is 66 cm. Its length is 10 times the width, find the sides of the rectangle.

Let’s compose a system of equations for this problem. Let us denote one side as a. Then the second side is equal to.

1) The perimeter is equal to the sum of the lengths of all sides: 2a + 2b = 66;

2) The length is 10 times the width: a = 10v;

3) System:

2a + 2b = 66;

a = 10b;

4) Let’s solve the system by substitution of variables. We have already expressed the variable a through the variable c. Now you can substitute it in the first expression:

2 * 10b+ 2b = 66;

5) Let us arrange the resulting equation:

22b = 66;

6) Find the variable b by reducing both sides of the equation by 22:

b = 3;

7) Find a: a = 10 * 3 = 30.

Answer: 30 and 3.