Find the length of the sides of a rectangle if its perimeter is 54 cm and the sides are 6: 3.

If the lengths of the sides of the rectangle are 6: 3, then this means that one side contains 6 parts, and the other side contains 3 of the same parts.

Let one part be x cm, then the length of one side of the rectangle is 6x cm, and the length of the second side of the rectangle is 3x cm.By the problem statement, it is known that the perimeter of the rectangle (the perimeter of the rectangle is the sum of the lengths of all sides of the rectangle; P = 2 (a + b)) is 2 (6x + 3x) cm or 54 cm.Let’s make an equation and solve it.

2 (6x + 3x) = 54;

2 * 9x = 54;

18x = 54;

x = 54: 18;

x = 3 (cm) – length of one part;

6x = 3 * 6 = 18 (cm) – the length of one side;

3x = 3 * 3 = 9 (cm) – the length of the second side.

Answer. 18 cm, 9 cm.