The lengths of the sides of the rectangle are 3: 4 if the perimeter of the rectangle is 56cm.

The perimeter of a rectangle is determined by the formula:

P = 2a + 2b.

Let’s find its sides, provided that they relate as 3: 4, and the sum of all sides = 56 cm, making the equation:

2 * 3x + 2 * 4x = 56. Let’s perform actions with the coefficients of the variable on the left side of the equation:

14x = 56.

X = 56: 14 = 4.

Therefore, the length is 4 * 4 = 16 cm and the width = 3 * 4 = 12 cm.