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In the diagram, $AB,$ $BC,$ $CD,$ $DE,$ $EF,$ $FG,$ $GH,$ and $HK$ all have length $4,$ and all angles are right angles, with the exception of the angles at $D$ and $F.$

 

If a perpendicular EM is drawn from E to DF (a close-up is shown below), and if x is the length of EM then what is X^2


 

 Mar 28, 2020
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The relationship EM^2=DM*MF is very helpful...

 

DF=\(4\sqrt{2}\), so \(DM=2\sqrt{2}\) and \(MF=2\sqrt{2}\).

 

\(EM^2=2\sqrt2*2\sqrt{2}\)

 

\(EM^2=8\)

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 Mar 28, 2020

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