Answer: 10*sqrt(30)
That is the same as writing [tex]10\sqrt{30}[/tex]
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Explanation:
The diagram shows that
That must mean DC = AC-AD = 60-50 = 10
We'll use this to help find BD as shown below
AD/BD = BD/DC
AD*DC = BD*BD .... cross multiply
(BD)^2 = AD*DC
BD = sqrt(AD*DC) ..... geometric mean formula
BD = sqrt(50*10)
BD = sqrt(500)
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Now apply the pythagorean theorem to find AB. Focus on triangle ABD.
(AD)^2 + (BD)^2 = (AB)^2
(AB)^2 = (AD)^2 + (BD)^2
(AB)^2 = (50)^2 + (sqrt(500))^2
(AB)^2 = 2500 + 500
(AB)^2 = 3000
AB = sqrt(3000)
AB = sqrt(100*30)
AB = sqrt(100)*sqrt(30)
AB = 10*sqrt(30)
