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Math Help - Relationship between a side and the area of a rectangle

  1. #1
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    Relationship between a side and the area of a rectangle

    I have a rectangle with sides "a" (width) and "b" (length).
    If I find the midpoint of "b" and draw a line from it to a corner ("c"), it forms a triangle with the sides a, b/2 and c.
    It is a right-angle triangle with c being the hypotenuse.
    Therefore a^2+(b/2)^2=c^2
    What is the relationship between side "c" and the area of the rectangle (ab)?
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  2. #2
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    Quote Originally Posted by psychoticmind View Post
    I have a rectangle with sides "a" (width) and "b" (length).
    If I find the midpoint of "b" and draw a line from it to a corner ("c"), it forms a triangle with the sides a, b/2 and c.
    It is a right-angle triangle with c being the hypotenuse.
    Therefore a^2+(b/2)^2=c^2
    What is the relationship between side "c" and the area of the rectangle (ab)?
    From the square

    (a+{b/2})^2 = a^2+ab+{b/2}^2

    then

    (a+{b/2})^2-ab = c^2
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