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

• Jul 5th 2009, 02:52 AM
olivia59
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
• Jul 5th 2009, 02:55 AM
malaygoel
The side of the larger square is x+y

Hence area of the large square=$\displaystyle (x+y)^2$
• Jul 5th 2009, 02:57 AM
olivia59
prove pythagoras theorem
Thanks. How do I Show how these results can be used to prove pythagoras theorem
• Jul 5th 2009, 02:58 AM
olivia59
and also how do i show it can be written as z²+2xy?
• Jul 5th 2009, 03:00 AM
malaygoel
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
=$\displaystyle z^2+4*\frac{1}{2}xy$
=$\displaystyle z^2+2xy$

pythagoras theorem: press spoiler

Spoiler:

$\displaystyle (x+y)^2=z^2+2xy$
$\displaystyle x^2 + y^2 =z^2$