Hello!
First, notice that as we have similar sides, we will also have similar sides. So:
EF is similar to HI
EG is similar to GH
FG is similar to GI
Notice that we know the measurement of four sides, so we can write it as a proportion, look:
[tex]\frac{EF}{HI}=\frac{EG}{GH}[/tex]
Replacing with the values:
[tex]\frac{3}{4}=\frac{x+1}{x+3}[/tex]
Multiplying it across:
[tex]\begin{gathered} 3\cdot(x+3)=4(x+1) \\ 3x+9=4x+4 \\ 9-4=4x-3x \\ 5=x \\ x=5 \end{gathered}[/tex]
Now, let's replace it to know the measurement of sides with unknowns (EG and GH):
[tex]\begin{gathered} EG=x+1 \\ EG=5+1 \\ EG=6 \\ \\ GH=x+3 \\ GH=5+3 \\ GH=8 \end{gathered}[/tex]
Right answer: third alternative.
