What is the value of x?

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1 Answer
CW
Feb 5, 2017

#x=3#

Explanation:

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Since #CD# bisects #angleACB#, by Angle bisector theorem, we know that:
#(BD)/(AD)=(BC)/(AC)#
#=> x/2.25=4/3, => x=(2.25*4)/3=3#

Alternative solution : using Sine Law
In #DeltaACD, 2.25/sina=3/sinb# ------------EQ(1)
In #DeltaBCD#, #x/sina=4/sin(180-b)#
As #sinb=sin(180-b)#
#=> x/sina=4/sinb# ------------------------EQ(2)

By dividing EQ(2) by EQ(1), we get:
#x/2.25=4/3#
#=> x=(2.25*4)/3=3#

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