Point C lies on the segment AB. Find the length of the segment AB if AC = 8 cm and the length

Point C lies on the segment AB. Find the length of the segment AB if AC = 8 cm and the length of the segment CB is 3 times the length of the segment AC.

We need to determine the length of the segment AB.

From the problem statement, we know that the point C belongs to the segment AB. Therefore, we can assert that the length of AB, will be calculated as follows:

AB = AC + CB

We know that the length of the segment AC is AC = 8 cm, and the length of the CB is 3 times the length of the segment AC. That is, we can write the following:

CB = AC * 3

Thus, we get that the length of the segment AB will be:

AB = AC + CB = AC + AC * 3 = AC * (1 + 3) = 4 * AC = 4 * 8 = 32 cm

That is, we got that the length of the segment AB is 32 cm.