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    "Jack wishes to build a wooden enclosure with a rectangular cross section and has available 3m of wood. If the lengths of the two sides of the rectangle are x and y;

    a) Find the area of the enclosure in terms of x
    b) hence find the maximum area that can be enclosed"

    This question has got me stumped; usually I can do these ones fine.

    Is the preamble bit saying that the Area = 3m
    Therefore 3m = xy, which can re-arrange to form y=3/x
    Therefore A=x(3/x)

    For B though, I'm sure you usually differentiate, let that equal 0 and solve to find the max value for X, then sub that into the equation from part a) to find the overall max value. However, x(3/x) differentiated is zero, thus i'm 'stumped'.

    Is my working wrong, or am I confused with the '3m = area' presumption?
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    Surely if 3m of wood is available, then that means that the perimeter is 3m, and not the area.
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    (Original post by Expendable)
    "Jack wishes to build a wooden enclosure with a rectangular cross section and has available 3m of wood. If the lengths of the two sides of the rectangle are x and y;

    a) Find the area of the enclosure in terms of x
    b) hence find the maximum area that can be enclosed"

    This question has got me stumped; usually I can do these ones fine.

    Is the preamble bit saying that the Area = 3m
    Therefore 3m = xy, which can re-arrange to form y=3/x
    Therefore A=x(3/x)

    For B though, I'm sure you usually differentiate, let that equal 0 and solve to find the max value for X, then sub that into the equation from part a) to find the overall max value. However, x(3/x) differentiated is zero, thus i'm 'stumped'.

    Is my working wrong, or am I confused with the '3m = area' presumption?
    It means that the perimeter of the enclosure is 3m. Work out what the perimeter of the enclosure is in terms of x and set it equal to 3m. Once you have this, you can work out an expression for the area of the enclosure and then you differentiate this, set it equal to zero and solve to get the max area.
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    Ah, I thought so - I forget the enclosure is basically hollow. Thank you
 
 
 
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Updated: March 26, 2011
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