Answer:
15
Explanation:
The Lengths EI and GI are equal; therefore,
[tex]\begin{gathered} EI=GI \\ 2t+9=9t-12 \end{gathered}[/tex]adding 12 to both sides gives
[tex]\begin{gathered} 2t+9+12=9t-12+12 \\ 2t+21=9t \end{gathered}[/tex]subtracting 2t from both sides gives
[tex]2t+21-2t=9t-2t[/tex][tex]21=7t[/tex]Finally, dividing both sides by 7 gives
[tex]\boxed{t=3.}[/tex]With the value of t in hand, we now find the length GI.
[tex]GI=9t-12[/tex]putting in the value of t gives
[tex]GI=9(3)-12[/tex][tex]GI=27-12[/tex][tex]\boxed{GI=15}[/tex]which is our answer!