The answer is 1000 ft, 800 ft, 600 ft.
Let:
a - the longest side
b - the middle side
c - the shortest side
The perimeter of a triangular plot of land is 2400 ft: P = 2400 ft
The perimeter of a triangle is P = a + b + c, thus a + b + c = 2400
The longest feet (a) is 200 ft less than twice the shortest (c): a = 2c - 200
The middle side (b) is 200 ft less than the longest side (a): b = a - 200
Now, we have the system of three equations:
a + b + c = 2400
a = 2c - 200
b = a - 200
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Substitute a from the second equation into the third equation:
b = 2c - 200 - 200 = 2c - 400
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Substitute a and b into the first equation:
(2c - 200) + (2c - 400) + c = 2400
2c - 200 + 2c - 400 + c = 2400
2c + 2c + c - 200 - 400 = 2400
5c - 600 = 2400
5c = 2400 + 600
5c = 3000
c = 3000/5
c = 600 ft
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Now, use c and substitute into the second and third equation:
a = 2c - 200
a = 2 * 600 - 200
a = 1200 - 200
a = 1000 ft
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b = a - 200
b = 1000 - 200
b = 800 ft
