<s>[INST] What is the value of $x$ in $ABCD$ rectangle where $AE = 4, BE = 6, CE=5$ and $DE = x$? 

In the diagram of rectangular $ABCD$, $AE=4, BE= 6, CE = 5$ and
  $DE=x$, find the value of $x$

Source: Bangladesh Math Olympiad 2015 Junior Catagory
I can not relate these information with $DE$. 
 [/INST] Another way is:
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$$\begin{cases}6^2=a^2+b^2\\ 5^2=b^2+c^2\\ x^2=c^2+d^2\\ 4^2=a^2+d^2\end{cases} \Rightarrow \\
x^2=(a^2+d^2)-(a^2+b^2)+(b^2+c^2)=\\
4^2-6^2+5^2=5 \Rightarrow x=\sqrt{5}.$$
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