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The perimeter of arectangular poultry farm is 38 meter . if 3 meter subtracted from its length and 2 meter from its breadth , the length will be two times the breadth .find the area of the farm

Sagot :

sqdancefan

Answer:

  82 2/9 square meters

Step-by-step explanation:

The problem statement gives us two relations between length and width. We can write those using equations and the variables L and W for length and widh, in meters.

  P = 2(L +W) . . . . . . formula for the perimeter of a rectangle

  38 = 2(L +W) . . . . . the perimeter is 38 meters

  (L -3) = 2(W -2) . . . . length less 3 is twice the difference of wdith and 2.

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Dividing the first equation by 2 gives ...

  19 = L +W

Solving this for L gives ...

  L = 19 -W

Substituting for L in the second equation, we have ...

  (19 -W) -3 = 2(W -2)

  16 -W = 2W -4 . . . . . . . simplify

  20 = 3W . . . . . . . . . . . add W+4

  W = 20/3 . . . . . . . . . divide by 3

  L = 19 -20/3 = 37/3 . . . . find L from W

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The area of the farm is the product of length and width:

  A = LW = (37/3 m)(20/3 m) = 740/9 m²

  A = 82 2/9 m²

The area of the farm is 82 2/9 square meters.

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