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Math Help - Co-ordinate geometry minimum problem?

  1. #1
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    Co-ordinate geometry minimum problem?

    The area of a rectangular block of land is 1000m2. If its length is x metres, find the block's dimensions if the perimeter is a minimum?

    I have to solve the problem using a composite graph and finding its minimum rathert than using calculus. It would be appreciated if you could help me as I'm really not sure how to approach this

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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Co-ordinate geometry minimum problem?

    Letting x be the length, I would then let y be the width, A be the area, and P be the perimeter.

    Can you give the area and perimeter in terms of x and y?
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  3. #3
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    Re: Co-ordinate geometry minimum problem?

    Thank you, I am so silly. I got to the stage of making an equation for the perimeter but broke down because I didn't know what to let it equal to (i.e. thanks to you, I just let it equal P and then subbed values)!

    Thanks, I got the (easy) answer!
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  4. #4
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    Re: Co-ordinate geometry minimum problem?

    Alternatively you can go as under:
    Area = length x breadth
    Let length = x m
    Thus 1000 = x * breadth : Thus breadth = 1000/x
    Perimeter P = 2 ( length + breadth ) = 2 ( x + 1000/x )
    now you can take it forward.
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