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 x denote one-fifth of the length of the longest midline of this triangle.

Then the length of the longest midline of this triangle should be 5x cm.

According to the condition of the problem, the middle lines of this triangle are related as 3: 3: 5, therefore, the lengths of the other two middle lines of the triangle should be equal to 3x cm and 3x cm.

Since in any triangle the lengths of the middle lines are equal to half the lengths of the corresponding sides of this triangle, the lengths of the sides of this triangle should be equal to 2 * 5x = 10x cm, 2 * 3x = 6x cm and 2 * 3x = 6x cm.

By the condition of the problem, the perimeter of the triangle is 88 cm, therefore, we can draw up the following equation:

10x + 6x + 6x = 88,

solving which, we get:

22x = 88;

x = 88/22 = 4.

Find the sides of the triangle:

10 * 4 = 40 cm;

6 * 4 = 24 cm;

6 * 4 = 24 cm.

Answer: 40 cm, 24 cm, 24 cm.