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    A variable rectangle has a constant perimeter of 20 cm. Find the lengths of the
    sides when the area is a maximum.

    I take it that the lengths of sides are the same as the x and y values for what would be the maximum point if we were talking about a parabola? However the part I don't understand it the first sentence.

    Any help would be appreciated, thanks.
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    (Original post by Kamila_Kamizaki)
    A variable rectangle has a constant perimeter of 20 cm. Find the lengths of the
    sides when the area is a maximum.

    I take it that the lengths of sides are the same as the x and y values for what would be the maximum point if we were talking about a parabola? However the part I don't understand it the first sentence.

    Any help would be appreciated, thanks.
    You have two equations,  A = xy and  2x + 2y = 20 \implies x + y = 10

    Solve these simultaneously and form a quadratic equation. Next, either differentiate or complete the square to find the maximum point.
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    (Original post by zeldor711)
    You have two equations,  A = xy and  x + y = 20

    Solve these simultaneously and form a quadratic equation. Next, either differentiate or complete the square to find the maximum point.
    Wouldn't it be 2x+2y=20? If no, why?
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    (Original post by Kamila_Kamizaki)
    Wouldn't it be 2x+2y=20? If no, why?
    You are correct
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    (Original post by Kamila_Kamizaki)
    Wouldn't it be 2x+2y=20? If no, why?
    Ahh yes, my mistake. Will edit
 
 
 
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