Question

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. ...?

Answer 1

The lengths of the three sides of the triangular plot are 600 feet for the shortest side, 800 feet for the middle side, and 1000 feet for the longest side.

Step-by-step explanation:

To find the lengths of the three sides of the triangular plot, let's define the shortest side as x. Therefore, according to the problem statement, the longest side would be 2x - 200 feet and the middle side would be (2x - 200) - 200 = 2x - 400 feet. The perimeter of the triangle is the sum of all its sides, which is given as 2400 feet.

The equation representing the perimeter of the triangle is:
x + (2x - 200) + (2x - 400) = 2400

Simplifying the equation, we get:
5x - 600 = 2400
Adding 600 to both sides:
5x = 3000

Dividing by 5 gives us:
x = 600

Thus, the shortest side is 600 feet, the longest side is 2(600) - 200 = 1000 feet, and the middle side is 1000 - 200 = 800 feet.

The lengths of the three sides of the triangular plot are 600 feet, 800 feet, and 1000 feet respectively.

Answer 2

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