The segment AB, the length of which is 20 cm, is divided by points K, M and P into 4 segments

The segment AB, the length of which is 20 cm, is divided by points K, M and P into 4 segments in the ratio 6: 8: 2: 9. How many centimeters is the length of the AP segment less than the length of the KB segment?

Let’s calculate how many conditional parts in total are summed up by all the resulting four parts, if it is known that the ratio of parts to each other is 6: 8: 2: 9:

1) 6 + 8 + 2 + 9 = 25 (h.)

Let’s find what the length of one such conditional part is equal to if the entire segment AB has a length of 20 cm:

2) 20/25 = 0.8 (cm).

We find what the length of the segment AR is equal to in conventional parts:

3) 6 + 8 + 2 = 16 (h.)

So the length of the AR is:

4) 0.8 * 16 = 12.8 (cm).

We find what the length of the KB segment is equal to in conventional parts:

3) 9 + 8 + 2 = 19 (h.)

So the length of the AR is:

4) 0.8 * 19 = 15.2 (cm).

The difference is:

5) 15.2 – 12.8 = 2.4 (cm).

Answer: 2.4 cm.