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Let p be the size of the smallest piece.

Then we know that it (p) plus the middle piece (p + 5) and the longest piece (3 x p) adds up to 75.

p + (p+5) + 3p = 75

=> 2p + 5 + 3p = 75

=> 5p = 75 - 5

=> 5p = 70

=> p = 14

So the smallest piece is p = 14 ft.

The middle piece is p + 5 = 19 ft.

And the largeset peice is 3p = 42 ft.

Adding the sizes to check: 14 + 19 + 42 = 75

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