what is the length 1 Attachment(s) What is x in the attached? All I can think of is to draw a line from A to E, but that doesn't seem to help much either. Answer is 2 * sqrt 6, but I do not know how they obtained this. 
1 Attachment(s) First off ABCD is a rectangle even if you choose not to draw it that way. Second with the information show the problem is indeterminate as the following picture illustrates. http://mymathforum.com/attachment.ph...1&d=1541684711 
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I disagree with the above. I doubt that it's intended that there are right angles at A and C, and even if there are, it doesn't seem to follow that ABCD is a rectangle. Also, the rectangle diagrams don't support BA = BE. However, a plausible diagram would be a good idea. 
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Do you think the square at A and C means those two angles are equal? 
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I think ketanco is mistaken. My analysis indicates that the angles at A and C are equal, but are not right angles. Also, a correct diagram is quite surprising and very different in appearance from the deliberately misdrawn diagram provided. However, I've not yet found a proof that the diagram I have in mind is unique. 
Connect B with D and let $\displaystyle BD=d$. Also, let $\displaystyle BA=BE=y$. Then from right triangle $\displaystyle ABD$ we get $\displaystyle x^2=d^2y^2$. From right triangle $\displaystyle BDC$ we get $\displaystyle BC^2=d^27^2$. From right triangle $\displaystyle BEC$ we get $\displaystyle BC^2=y^25^2$. So, $\displaystyle d^249=y^225$ and $\displaystyle d^2y^2=4925=24$. Thus, $\displaystyle x^2=24$ and $\displaystyle x=2 \sqrt{6}$. 
1 Attachment(s) Here is a picture. Attachment 10018 
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