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Math Help - Please help....tricky question

  1. #1
    Junior Member
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    Vadodara,Gujarat,India
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    Please help....tricky question

    Find all sides of rectangle having integral sides whose area is numerically equal to perimeter?
    I also want the mathematical proof
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  2. #2
    MHF Contributor red_dog's Avatar
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    Medgidia, Romania
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    Let a and b be the sides of the rectangle. Then

    2a+2b=ab\Rightarrow a=\frac{2b}{b-2}=2+\frac{4}{b-2}

    Then b-2 must be a positive divisor of 4.

    Take all possible cases: b-2=1, b-2=2, b-2=4. Find b and then find a.
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