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In triangle ABCABCABC, ∠B=90∘,BE=3, \angle B = 90 ^ \circ, BE = 3, ∠B=90∘,BE=3, and BD=4BD = 4 BD=4.
If AE=ED=DC AE = ED = DC AE=ED=DC, then the value of ACACAC can be expressed as ab a \sqrt{b} ab, where aaa and bb b are positive integers and bbb is square-free.
Find a+b a+b a+b.
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