Let: a - the longest side b - the middle side c - the shortest side
The <span>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
</span><span>The longest feet (a) is 200 ft less than twice the shortest (c): a = 2c - 200 </span><span>The middle side (b) is 200 ft less than the longest side (a): b = a - 200
Now, we have the system of three equations: </span>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
