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Math·Geometry and Trigonometry·Right triangles and trigonometry

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In quadrilateral $KLMN$ shown, $KL=3,LM=3,KN=27$, and $MN=27$. Diagonals $KM$ and $LN$ (not shown) intersect at point $G$ (not shown), where $GK=1$ and $GM=1$. If the length of diagonal $LN$ is $\sqrt{p}+\sqrt{w}$, where $p$ and $w$ are integers, what is the value of $p+w$?

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