Point P belongs to the segment SM, the length of which is 10 cm. Find the lengths of the segments SP

Point P belongs to the segment SM, the length of which is 10 cm. Find the lengths of the segments SP and PM if the difference between the lengths of the segments SP and PM is 2.2 cm.

1. Let us denote the length of the segment PM by x.

2. Determine the length of the segment SP:

SP = x + 2.2 cm.

3. Segment SM = PM + SP, according to the condition, its length is 10 cm, compose and solve the equation:

x + x + 2.2 = 10;

2x + 2.2 = 10;

2x = 10 – 2.2;

2x = 7.8;

x = 7.8: 2;

x = 3.9.

4. The length of the PM segment is 3.9 cm.

5. What is the length of the SP segment?

3.9 + 2.2 = 6.1 (cm).

Answer: the lengths of the segments SP and PM are 6.1 cm and 3.9 cm, respectively.