Show that the area of the large square in the diagram can be written as (x+y)², and.. - Math Help Forum

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#1

$Old$ July 5th, 2009, 04:52 AM

olivia59 $olivia59 is offline$

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$Default$ Show that the area of the large square in the diagram can be written as (x+y)², and..

Show that the area of the large square in the diagram can be written as (x+y)², and also as z²+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

$Old$ July 5th, 2009, 04:55 AM

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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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$Old$ July 5th, 2009, 04:57 AM

olivia59 $olivia59 is offline$

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$Default$ prove pythagoras theorem

Thanks. How do I Show how these results can be used to prove pythagoras theorem

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$Old$ July 5th, 2009, 04:58 AM

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and also how do i show it can be written as z²+2xy?

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$Old$ July 5th, 2009, 05:00 AM

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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:

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