Question

What is the value of x?

Answer 1

`x=3`

Explanation:

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`