For this you would use the "angle bisector theorem," which states that the ratio of the other two sides are proportional to the two segments of the divided base (opposite the bisected angle). See attached image...
In other words:
[tex] \frac{3}{4} = \frac{2.25}{x} \\ cross - multiply \\ 3x = 4(2.25) \\ x = 9 \div 3 = 3[/tex]
