Rectangle ADCD contains a point X such that AX=3, BX=4, and CX=5. Find DX.
By the British Flag Theorem, if \(X\) is a point in the interior of a rectangle \(ABCD\), then $$AX^2+CX^2=BX^2+DX^2.$$
It follows that $$9+25=16+DX^2 \implies DX^2=18 \implies DX = \boxed{3\sqrt{2}}.$$
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