Answer:
Width = 200 meters
Length = 600 meters
Explanation:
We can find the length and width of the pasture using a system of equations, where:
- L represents the length of the pasture,
- and W represents the width of the pasture.
First equation:
Since we're told that the pasture's length is 3 times its width, our first equation is given by:
L = 3W
Second equation:
The formula for the perimeter of a rectangle is given by:
P = 2L + 2W, where:
- P is the perimeter,
- L is the length,
- and W is the width.
Since we're told that the perimeter of the pasture is 1600 meters, our second equation is given by:
P = 2L + 2W
Method to solve: Substitution:
Solving for W:
We can first solve for W by substituting 3W for L in 1600 = 2L + 2W:
1600 = 2(3W) + 2W
1600 = 6W + 2W
(1600 = 8W) / 8
200 = W
Thus, the width of the pasture is 200 meters.
Solving for L:
Now, we can find solve for L by plugging in 200 for W in L = 3W:
L = 3(200)
L = 600
Thus, the length of the pasture is 600 meters.