Answer :
Parameters Provided:
[tex]\begin{gathered} FG=12 \\ YZ=18 \\ \triangle\text{EFG }\cong\triangle\text{XYZ} \end{gathered}[/tex]The diagram of the question is shown below:
For similar triangles, the ratios of any two corresponding sides are equal. Hence, we can postulate from the image above that:
[tex]\frac{FR}{FG}=\frac{YS}{YZ}\text{ ----------(A)}[/tex]The values of FG and YZ are given already in the question.
To get FR and YS, we are told FR is 1 less than YS. Therefore,
[tex]FR=YS-1[/tex]Substituting these values into equation A, we have:
[tex]\frac{YS-1}{12}=\frac{YS}{18}[/tex]Multiply both sides by (12 x 18):
[tex]\begin{gathered} \frac{YS-1}{12}\times12\times18=\frac{YS}{18}\times12\times18 \\ 18(YS-1)=YS\times12 \\ 18(YS)-18=12(YS) \end{gathered}[/tex]Collecting like terms:
[tex]\begin{gathered} 18(YS)-12(YS)=18 \\ 6(YS)=18 \\ YS=\frac{18}{6} \\ YS=3 \end{gathered}[/tex]To get FR:
[tex]\begin{gathered} FR=YS-1 \\ FR=3-1 \\ FR=2 \end{gathered}[/tex]Therefore, the lengths of the medians are:
[tex]\begin{gathered} YS=3 \\ FR=2 \end{gathered}[/tex]