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Ludwig the cow has decided to build a rectangular fence around his part of a pasture because Gustav the goat thinks he is cool and can eat all the grass he wants, including the grass on Ludwig’s side of the pasture. Ludwig determines that the perimeter of the fence has to be greater than 132 yards. If Ludwig needs the width of the fence to be eight less than the length, determine, to the nearest whole yard, the smallest the length of the fence can be and still have a perimeter greater than 132 yards.

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sqdancefan

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Answer:

  38 yards

Step-by-step explanation:

Let x represent the length and y the width, both in yards. Then the required relations are ...

  2(x+y) > 132 . . . . . . the perimeter is greater than 132 yards

  y = x - 8 . . . . . . . . . . width is 8 less than length

Substituting for y in the first equation gives ...

  2(x +(x -8)) > 132

  4x -16 > 132

  x -4 > 33

  x > 37

The smallest length the fence can be is 38 yards.

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Check

At that length, the width is 30 yards, and the perimeter is 2(38+30) = 136 yards. If the length were 37 yards, the perimeter would be 132 yards, which is not greater than 132 yards.

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