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Math Help - Show that the area of the large square in the diagram can be written as (x+y), and..

  1. #1
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    Show that the area of the large square in the diagram can be written as (x+y), and..

    Show that the area of the large square in the diagram can be written as (x+y), and also as z+2xy?


    HERE IS THE DIAGRAM http://img43.imageshack.us/img43/9428/trig.png

    Do not use pythagoras theorem.

    b) Show how these results can be used to prove pythagoras theorem
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  2. #2
    Super Member malaygoel's Avatar
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    The side of the larger square is x+y

    Hence area of the large square= (x+y)^2
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  3. #3
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    prove pythagoras theorem

    Thanks. How do I Show how these results can be used to prove pythagoras theorem
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  4. #4
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    and also how do i show it can be written as z+2xy?
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  5. #5
    Super Member malaygoel's Avatar
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    Inside the larger square,
    there is a square of side z, and four right triangles of side x,y.

    total area=square of side z+4*area of triangles
    = z^2+4*\frac{1}{2}xy
    = z^2+2xy

    pythagoras theorem: press spoiler

    Spoiler:


    (x+y)^2=z^2+2xy
    x^2 + y^2 =z^2

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