What's the length of the |BC| ?

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1 Answer
CW
Sep 18, 2017

#BC=3sqrt10# units

Explanation:

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Consider #DeltaABH#, by Pythagorean Theorem,
#AB^2=AH^2+BH^2#
#=> AB=sqrt(3^2+6^2)=sqrt45=3sqrt5#
As #DeltaABH and DeltaDBA# are similar,
#=> (AD)/(AB)=(HA)/(HB)#
#=> AD=(HA)/(HB)*AB=3/6*3sqrt5=(3sqrt5)/2#
Given #AD=DC, => AC=2AD=3sqrt5#
As #AC=AB, and angleA=90^@#,
#=> angleABC=angleACB=45^@#
#=> DeltaABC# is an isosceles right triangle.
#=> BC=ABsqrt2=3sqrt5*sqrt2=3sqrt10#

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