A 32cm segment AB is divided into three parts, the lengths of which are 4: 7: 5. Find the lengths of these parts.

1. Let’s denote one part by x.

2. Let’s define the first part of the segment:

4 * x = 4x.

3. Let’s write down the second part of the segment:

7 * x = 7x.

4. Determine what the third part of the segment is equal to:

5 * x = 5x

5. Let’s compose and solve the equation:

4x + 7x + 5x = 32;

16x = 32;

x = 32: 16;

x = 2.

6. One part is equal to x = 2.

7. What is the length of the first part of the segment?

4 * x = 4 * 2 = 8 cm.

8. What is the length of the second part of the segment?

7 * x = 7 * 2 = 14 cm.

9. What is the length of the third part of the line segment?

5 * x = 5 * 2 = 10 cm.

Answer: segment AB is divided into parts 8 cm, 14 cm, 10 cm.