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Let 'x' be the factor to consider
since it is in the ratio of 4:5:6 then you'll have the lengths as
4x = shortest length 
5x = second longest length
6x = longest length
since you're given the total length of 75meters then you'll have it as:
4x + 5x + 6x = 75
15x = 75
 x = 5
since you are asked for the longest piece, then
6x = 6(5)
    = 30 meters
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