The length of the segment AB = 2x cm, the length of the BC = 3x cm, and the length of the CD = 5x cm

The length of the segment AB = 2x cm, the length of the BC = 3x cm, and the length of the CD = 5x cm. Find the length of the BC if AD = 40cm.

From the condition of the problem it can be seen that the segment AD was divided into 3 parts and it consists of segments: AB, BC and CD.

So the length of the entire segment AD is equal to:

AD = AB + BC + CD;

2x + 3x + 5x = 40;

10x = 40;

x = 4.

Now we can find the length of the BC:

BC = 4 * 3 = 12 cm.

Answer: BC = 12 cm.