Points C and D are marked on the segment AB, and the distance between points A and C is 2 cm 5 mm

Points C and D are marked on the segment AB, and the distance between points A and C is 2 cm 5 mm, the distance between points C and D is 2 times the distance between points A and C, and the distance between points D and B is 3 cm 5 mm less distance between points C and D. Find the distance between points A and B.

Let us express the distances in millimeters:

1 cm = 10 mm;

2 cm 5 mm = 2 * 10 + 5 mm = 20 mm + 5 mm = 25 mm;

3 cm 5 mm = 3 * 10 + 5 mm = 30 mm + 5 mm = 35 mm.

Let’s calculate the distance between points C and D:

25 mm * 2 = 50 mm is the distance between points C and D.

Let’s calculate the distance between points D and B:

50 mm – 35 mm = 15 mm is the distance between points D and B.

Let’s calculate the distance between points A and D:

25 mm + 50 mm = 75 mm is the distance between points A and D.

Let’s calculate the length of the segment AB:

75 mm + 15 mm = 90 mm – the length of the segment AB.

Let us express the length of the segment AB in centimeters:

90 mm = 90: 10 = 9 cm – the length of the segment AB.

Answer: the length of the segment AB is 90 mm or 9 cm.