Answer
$\overline{EB}$
Work Step by Step
AD$^{2}$+AC$^{2}$=DC$^{2}$
4$^{2}$+7$^{2}$=DC$^{2}$
16+49=DC$^{2}$
DC=$\sqrt {65}$$\approx$8.1
AE$^{2}$+AB$^{2}$=EB$^{2}$
7$^{2}$+5$^{2}$=EB$^{2}$
49+25=EB$^{2}$
EB=$\sqrt {74}$$\approx$8.6
EB$\gt$DC