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The length of a rectangular pasture is 3 times the width. the perimeter of the pasture is 1600 meters. what is the length and width of the pasture?

User Baretta
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1 Answer

4 votes

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.

User HpTerm
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