Geometry question. Please help?

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1 Answer
sankarankalyanam
Feb 16, 2018

#x = 5, bar(BC) = 24#

Explanation:

Given : AD is angular bisector of #hatA#

Using angle bisector theorem,

#(BD) / (AB) = (CD) / (AC)#

#(2x - 1) / 9 = (cancel(3) x) / cancel(15)^color(red)5 = x / 5#

#(2x - 1) / x = 9/5#

#2 - 1/x = 9/5#

#1/x = 1/5#, #color(green)(x = 5#

#BC = BD + CD = (2x - 1) + 3x = 10 - 1 + 15 = 24#

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