The middle lines of the triangle are 3: 3: 5, and the perimeter of the triangle is 88 cm. Find the sides of the triangle.

Let k be the coefficient of proportionality, then the middle lines of the triangle will be respectively equal to 3k; 3k; 5k, since by condition, the middle lines of a triangle are related as 3: 3: 5. By the property of the middle line of a triangle, the side of a triangle parallel to it has a length 2 times longer than the length of the middle line. This means that the sides of the triangle will have lengths of 6k; 6k; 10k. By condition, the perimeter of the triangle is 88 cm. Knowing this, we make the equation: 6k + 6k + 10k = 88; 22k = 88; k = 88: 22; k = 4 (cm). Then the sides of the triangle will be 6k = 6 ∙ 4 = 24 (cm); 6k = 6 ∙ 4 = 24 (cm); 10k = 10 ∙ 4 = 40 (cm).
Answer: The sides of the triangle are 24 cm, 24 cm and 40 cm long.