The perimeter of a triangular plot of land is 2400 ft. the longest feet is 200 ft less than twice the shortest. the middle side is 200 ft less than the longest side. find the lengths of the three sides of the triangular plot.

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

Substitute a from the second equation into the third equation:
b = 2c - 200 - 200 = 2c - 400

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

Now, use c and substitute into the second and third equation:
a = 2c - 200
a = 2 * 600 - 200
a = 1200 - 200
a = 1000 ft
___
b = a - 200
b = 1000 - 200
b = 800 ft

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