Two triangles that are similar have the following characteristics:
1) The corresponding angles are congruent
2) The corresponding sides ratios have the same proportion.
So for triangles, JKL and J'K'L' the ratios of the corresponding sides are:
[tex]\frac{J^{\prime}K^{\prime}}{JK}=\frac{K^{\prime}L^{\prime}}{KL}=\frac{J^{\prime}L^{\prime}}{JL}[/tex]
Given
JK=10cm
KL=30cm
K'L'=13.5cm
We can calculate the length of J'K' using the ratios:
[tex]\begin{gathered} \frac{K^{\prime}L^{\prime}}{KL}=\frac{J^{\prime}K^{\prime}}{JK} \\ \frac{13.5}{30}=\frac{x}{10} \\ (\frac{13.5}{30})\cdot10=x \\ x=4.5 \end{gathered}[/tex]
Segment J'K'=4.5cm
