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a rectangular lot whose perimeter is 400 feet is fenced along three sides. an expensive fencing along the lot's length costs $22 per foot , and an inexpensive fencing along the two side widths costs only $8 per foot. the total cost of the fencing along the three sides comes to $3920. what are the lot's dimensions?

User Shijing Lv
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Final answer:

The lot's dimensions are approximately 165.72 feet in length and 17.14 feet in width. This was determined by solving a system of equations derived from the perimeter and total cost of fencing provided in the question.

Step-by-step explanation:

To find the dimensions of the rectangular lot, let's define length (l) as the side with the expensive fencing and width (w) as the other two sides. The perimeter (P) is given by the formula 2l + 2w = P. However, since only three sides are fenced, we will use l + 2w = P/2.

Given that the perimeter is 400 feet, the equation simplifies to l + 2w = 200. Furthermore, the cost of fencing totals $3920, where expensive fencing costs $22 per foot along the length and inexpensive fencing costs $8 per foot along the widths. The cost equation can then be written as 22l + 8(2w) = 3920.

Let's solve this system of equations:

  1. l + 2w = 200
  2. 22l + 16w = 3920

Multiply the first equation by -22 to eliminate l:

  1. -22l - 44w = -4400
  2. 22l + 16w = 3920

Add both equations:

-28w = -480

Divide by -28 to find w:

w = 17.14

Substitute w into the first equation to find l:

l + 2(17.14) = 200

l = 200 - 34.28

l = 165.72

Thus, the dimensions of the lot are approximately a length of 165.72 feet and a width of 17.14 feet.

User David Kierans
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