Point M divides the segment AB into 2 segments: AM and MB. The AM segment is 5 times longer than the MB

| January 29, 2021 | education

Point M divides the segment AB into 2 segments: AM and MB. The AM segment is 5 times longer than the MB segment, and the MB segment is 24 mm shorter than the AM segment. Find the length of the segment AM, MB, AB.

Let x be the length of the MВ segment. Since the AM segment is five times longer than the MB segment, the AM segment is equal to: 5 * x. And since the MВ segment is shorter than the AM segment by 24 mm, the AM segment is 24 mm. We have the equation: 5x = x + 24. Move all the unknown terms of the equations to the left side, and all the known terms of the equation to the right: 5x – x = 24, 4x = 24, x = 24: 4, x = 6 mm. The length of the MB segment is 6 mm, then the length of the MB segment is: 6 mm * 5 = 30 mm. And the length of the segment AB = AM + MB = 6 mm + 30 mm = 36 mm.
Answer: AB = 36 mm, AM = 6 mm, MВ = 30 mm.



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