Answer: E. sqrt(45)
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The right triangles are similar, allowing us to form the proportion below
BD/AD = AD/DC
5/AD = AD/9 .... substitution
5*9 = (AD)*(AD) .... cross multiply
45 = (AD)^2
(AD)^2 = 45
AD = sqrt(45) ... apply square root
We could simplify but your teacher has decided not to. If you want to simplify, then
AD = sqrt(45)
AD = sqrt(9*5)
AD = sqrt(9)*sqrt(5)
AD = 3*sqrt(5)
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Segment AD is the geometric mean of BD and DC.
AD = sqrt(BD*DC)
which is the result of solving BD/AD = AD/DC for AD
So,
AD = sqrt(BD*DC)
AD = sqrt(5*9)
AD = sqrt(45)
