38
Step-by-step explanation:
Since the polygons are similar, the corresponding sides are all in the same proportions.
x-2/4.5 = 16/2 = 48/6
Solving for x
[tex]\frac{x-2}{4.5}=\frac{48}{6}[/tex]
[tex]\frac{x-2}{4.5}=8[/tex]
[tex]\frac{4.5\left(x-2\right)}{4.5}=8\cdot \:4.5[/tex]
[tex]x-2=36[/tex]
[tex]x-2+2=36+2[/tex]
[tex]x=38[/tex]
Therefore, the value of x is 38