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In a square $ABCD$, say there is a point $P$ which lies inside it, the point $P$ is located at distances $x$, $y$ and $z$ meters from $A,B$ and $C$ respectively.

Using this information how could we compute a form for the area of the square?Please explain your approach.

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    How about *hacking* it out? Assume that the vertices are $(0,a), (0,0), (a,0), (a,a)$ and P is $(u,v)$. Then $u^2+(v-a)^2=x^2, u^2+v^2=y^2, (u-a)^2+v^2=z^2$. You can subtract (2) from (1) and (3) to solve for $(u,v)$ in terms of $a$. Plugging that in (2) should give you $a$. :-)2011-09-16

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