A 32 cm segment AB is divided into 3 parts, the lengths of which are 4: 7: 5. Find the lengths of these pieces.

It is known from the condition that the segment AB with a length of 32 cm is divided into 3 parts. It is also known that the lengths of the parts are related as 4: 7: 5. In order to find the lengths of these parts, we compose and solve the equation.

Let’s denote by x the coefficient of similarity. Then we can write the lengths of the parts of the segments as 4x, 7x and 5x.

Knowing the length of the entire segment, we get the equation:

4x + 7x + 5x = 32;

We solve the linear equation:

16x = 32;

x = 32: 16;

x = 2.

The lengths of the parts of the segments: 4 * 2 = 8 cm, 7 * 2 = 14 cm, 5 * 2 = 10 cm.

Answer: 8, 10 and 14 cm.