The length of the segment AB is equal to 40 cm. Points of the CD divide the segment AB into segments AC, CD, DB.

The length of the segment AB is equal to 40 cm. Points of the CD divide the segment AB into segments AC, CD, DB. The length of the segment AB is 4 cm longer than the length of the segment AC, but 2 times less than the length of the segment DB. Find the length of the segment AC.

Let points C and D be marked on a segment AB 40 cm long so that they divide segment AB into segments AC, CD, DB, and AC = x cm, then:

4 + x (cm) – the length of the CD segment, since the length of the CD segment is 4 cm longer than the length of the AC segment;

(4 + x) ∙ 2 = 8 + 2 ∙ x (cm) – the length of the segment DВ, since the length of the segment CD is 2 times less than the length of the segment DB.

Knowing that the length of the segment is equal to the sum of the lengths of its parts, we compose the equation:

x + (4 + x) + (8 + 2 ∙ x) = 40;

4 ∙ x = 28;

x = 7 (cm) – the length of the segment AB.

Answer: The length of the AC segment is 7 cm.