△VAT≅△BDT. What is length of BT?
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we know that
If △VAT≅△BDT, then the corresponding sides will be congruent
[tex]VT=BT\\VA=BD\\ AT=DT[/tex]
we have
[tex]VT=6.3\ unit\\VA=3.7\ unit\\AT=4.7\ unit[/tex]
so
[tex]BT=6.3\ unit[/tex]
therefore
the answer is
[tex]BT=6.3\ unit[/tex]