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The solid below is a cube with volume 64 cubic inches.

If point E is the midpoint of edge $ {\overline { BD } } $, what is the perimeter of $ \Delta $ACE, in inches?

$10$

$ 4 + 4{\sqrt { 2 } } $

$ 4 + 4{\sqrt { 3 } } $

$12$

$ 4 + 4{\sqrt { 5 } } $