# On the segment AB, the length of which is 6 cm, two points M and K are marked.

On the segment AB, the length of which is 6 cm, two points M and K are marked. It is known that BM = 2BK; AM = 0.8 AK. Find the length of the MK segment.

1. Let us denote the length of the segment BK by the index “a”.

2. ВM = 2a.

3. AM = AB – BM = 6 – 2a.

4. AK = AB – ВK = 6 – a.

5. AM = 0.8AK (according to the problem statement).

AM = 0.8 (6-a).

6. Equate the right-hand sides of the equations from points 3 and 5:

(6 – 2a) = 0.8 (6-a). 1.2a = 1.2. a = 1 centimeter.

The length of the ВC segment is 1 centimeter.

7. Since the length of the ВM = 2ВK (according to the condition of the problem), then MK = ВK = 1 centimeter.

Answer: the length of the MK segment is 1 centimeter.

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