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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