Point C is marked on the segment AB so that AB: BC = 6: 5. Find the length of the segment BC if AC = 22cm.

It is known from the condition that a point C is marked on the segment AB so that AB: BC = 6: 5. And you need to find the length of the segment BC if AC = 22 cm.

To solve the problem, we will compose and solve the equation.

We will start by introducing the similarity coefficient x and then the lengths of the segments can be written as:

CB = 5x and AB = 6x.

It is known from the condition that the segment:

AB = AC + CB.

Let’s write the equation:

6x = 22 + 5x;

We solve it:

6x – 5x = 22;

x = 22 cm.

Now we find the length of the segment CB = 5x = 5 * 22 = 110 cm.

Answer: the length of the segment CB = 110 cm.