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Math Help - rectangle with unknown sides?

  1. #1
    Junior Member risteek's Avatar
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    rectangle with unknown sides?

    Ok we have this rectangle questiosn that makes no sense to me.

    Here is a diagram of the question


    The smaller rectangle is 4 by 5 metres which the area would be 20 metres. Then the rectangle 'grows' bigger and then has an area of 56mē. How do I get the length and the width of the second rectangle? I think I know the answer but I don't know how to get it.

    Any help is greatly appriciated, thanks!
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  2. #2
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    earboth's Avatar
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    Quote Originally Posted by risteek View Post
    Ok we have this rectangle questiosn that makes no sense to me.

    Here is a diagram of the question


    The smaller rectangle is 4 by 5 metres which the area would be 20 metres. Then the rectangle 'grows' bigger and then has an area of 56mē. How do I get the length and the width of the second rectangle? I think I know the answer but I don't know how to get it.

    Any help is greatly appriciated, thanks!
    Let's assume that the sides increse by a constant factor k. (The question doesn't state that the ratio of length to width is a constant!)

    Then you know about the new length L = 5k and the new width W = 4k and therefore

    5k \cdot 4k = 56~\implies~ 20k^2 = 56~\implies~ k^2 = 2.8

    and therefore the dimensions of the new rectangle are:

    (5 \cdot \sqrt{2.8}) \cdot (4 \cdot \sqrt{2.8})=56
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  3. #3
    Junior Member risteek's Avatar
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    Thank you for your help! It means a lot! =)
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