Answers:
shortest side = 20 feet
medium side = 26 feet
longest side = 34 feet
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Explanation:
x = first side
y = second side
z = third side
Assume x < y < z
y = x+6 since the second side is 6 ft longer than the shortest (first) side
z = 2x-6 because "third side that is 6 feet shorter than twice the length of the shortest side"
P = 80 is the perimeter
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x+y+z = P
x+x+6+z = P .... plug in y = x+6
2x+6+2x-6 = P ... plug in z = 2x-6
4x = P
4x = 80 ... plug in P = 80
x = 80/4 ... divide both sides by 4
x = 20
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first side = x = 20 feet
second side = y = x+6 = 20+6 = 26 feet
third side = z = 2x-6 = 2*20-6 = 34 feet
So,
x = 20, y = 26, z = 34
are the three side lengths
x+y+z = 20+26+34 = 80
and the three side lengths add to 80, so the answer checks out
