Answer: 8.2 (choice B)
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Step-by-step explanation:
First we'll need the length of segment BD, which I'll call x for now. The similar triangles allow us to set up the proportion below to solve for x
AD/BD = BD/DC
13/x = x/4
13*4 = x^2
52 = x^2
x^2 = 52
x = sqrt(52)
Segment BD is exactly sqrt(52) units long.
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Now focus your attention on triangle BDC. We'll use the pythagorean theorem to find BC
(BD)^2 + (DC)^2 = (BC)^2
( sqrt(52) )^2 + ( 4 )^2 = ( m )^2
52 + 16 = m^2
68 = m^2
m^2 = 68
m = sqrt(68)
m = 8.2462 approximately
m = 8.2