Answer:
|EF|=18
Step-by-step explanation:
Using the mid-segment theorem of a trapezoid, [tex]|EF|=\frac{1}{2}(|AD|+|BC|)[/tex]
We substitute the expressions for the sides and solve for x.
[tex]4x+6=\frac{1}{2}(6+9x+4)[/tex]
This implies that:
[tex]4x+6=\frac{1}{2}(9x+9)[/tex]
Multiply through by 2 to get:
[tex]8x+12=9x+9[/tex]
Group and combine like terms to get:
[tex]12-9=9x-8x[/tex]
[tex]x=3[/tex]
[tex]|EF|=4(3)+6=18[/tex]
