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Nataly_w [17]
3 years ago
15

A dairy farmer plans to enclose a rectangular pasture adjacent to a river. To provide enough grass for the herd, the pasture mus

t contain 18 square meters. No fencing is required along the river. What dimensions will use the least amount of fencing?
Mathematics
1 answer:
AysviL [449]3 years ago
3 0

Answer:

390 m (perpendicular to river) x 780 m (parallel to river)

Step-by-step explanation:

Let y be the length of the side parallel to the river, and let x be the length of the sides perpendicular to the river.

The total area and length of fence required are given by:

Rewriting the length of fence as a function of only x:

The value of x for which the derivate of L(x) is zero is the length of x that uses the least amount of fencing:

If x = 390 m, then:

The dimensions that will use the least amount of fencing are 390 m x 780 m

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The 40 feet of fencing which covers at least 182 square feet gives the possible lengths of x as x ≥ 13 or x ≤ 7

<h3>How can the area be expressed as an inequality?</h3>

Length of the fencing = 40 feet

Number of sides covered = Three sides

Area of the fencing ≥ 182 square feet

Length of the shorter side of the pen = x

The area is therefore;

  • x × (40 - 2•x) ≥ 182

2•x² - 40•x + 182 ≥ 0

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2•(x² - 13•x - 7•x + 91) ≥ 0

2•(x•(x - 13) - 7•(x - 13) ≥ 0

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Which gives;

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