Geometry question. Please help?

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Answer 1 · 2018-02-16T08:00:28

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

Given : AD is angular bisector of $hatA$

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

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

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

$2 - 1/x = 9/5$

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

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