Since triangles IJK and LMN are similar, the ratio between their corresponding sides is constant; then,
[tex]\frac{LM}{IJ}=\frac{MN}{JK}=\frac{NL}{KI}[/tex]Thus,
[tex]\begin{gathered} \Rightarrow\frac{x}{4}=\frac{29}{9} \\ \text{because} \\ MN=x,LM=29,JK=4,IJ=9 \end{gathered}[/tex]Therefore, solving for x,
[tex]\begin{gathered} \Rightarrow x=\frac{29}{9}\cdot4=12.888\ldots \\ \Rightarrow x\approx12.9 \end{gathered}[/tex]Hence, the answer is 12.9