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Math Help - EQ Triangle and square with same area

  1. #1
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    EQ Triangle and square with same area

    The area of an equilateral triangle (A ft2) is equal to that of a square. What is the length of the diagonal of the square?


    A. (2A) ft
    B. A ft
    C. (3A) ft
    D. 2(A) ft
    E. (5A) ft


    I know how to get there, but not sure if it's a correct path (i.e. is there a better way to solve it.)




    Forget the triangle, the area of both = A, and for the square A=s^2




    Length of a diagonal of a square is S*2


    Which we can see is A*2=(2A)
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  2. #2
    MHF Contributor Amer's Avatar
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    the diagonal of a square can be expressed d=(s^2+s^2)^(1/2) s is the square side
    and s^2 is the area of the square so it is equal A

    d=\sqrt{s^2+s^2}=\sqrt{A+A}=\sqrt{2A}

    see this for more explanation

    EQ Triangle and square with same area-triangle.jpg
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  3. #3
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    That's much more direct, thanks.
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