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7 June, 07:33

Farmer Ed has7500 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, what is the largest area that can be enclosEd?

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  1. 7 June, 07:38
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    First let's find out what would the sides of a square be.

    7500 / 4 = 1875

    Now we have 1875 as the sides and double at the top.

    So 1875 * 3750 = 7031250 meters squared
  2. 7 June, 07:42
    0
    7,031,250 m^2

    Step-by-step explanation:

    We know that:

    Area of a rectangle = length x width

    Also, since the rectangular plot shares a border with a river so Farmer Ed only needs to fence rest of the three sides therefore, we can write it as:

    F = x + 2y

    7500 = x + 2y

    Solving this equation for x, we get:

    x = 7500 - 2y - - - (i)

    Now substitute this value of x in the Area of rectangle:

    Area = (7500 - 2y) * y

    Area = - 2y^2 + 7500y - - - (ii)

    The coefficient of - 2 means that the largest area will be at:

    -7500 / [2 (-2) ] = 1875 so y = 1875

    So substituting this value of y in the equation (i) we get:

    x = 7500 - 2 (1875)

    x = 7,031,250 m^2
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