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Parallelogram $EUCD$ has an area of $180\sqrt { 3 }$ square inches.

What is the perimeter of $EUCD$?

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$12\sqrt { 2 }$ inches

$15\sqrt { 2 }$ inches

$54\sqrt { 2 }$ inches

$18\sqrt { 2 }+6\sqrt { 6 }$ inches

$54\sqrt { 2 }+6\sqrt { 6 }$ inches