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. ...?
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
