Question

Assume triangle EFG is similar to triangle XYZ with medians line FR and line YS to sides line EG and line XZ respectively, FG =12 and YZ=18. If FR is 1 less than YS, find both medians

Answer 1

Parameters Provided:

`\begin{gathered} FG=12 \\ YZ=18 \\ \triangle\text{EFG }\cong\triangle\text{XYZ} \end{gathered}`

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:

`(FR)/(FG)=(YS)/(YZ)\text{ ----------(A)}`

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,

`FR=YS-1`

Substituting these values into equation A, we have:

`(YS-1)/(12)=(YS)/(18)`

Multiply both sides by (12 x 18):

`\begin{gathered} (YS-1)/(12)*12*18=(YS)/(18)*12*18 \\ 18(YS-1)=YS*12 \\ 18(YS)-18=12(YS) \end{gathered}`

Collecting like terms:

`\begin{gathered} 18(YS)-12(YS)=18 \\ 6(YS)=18 \\ YS=(18)/(6) \\ YS=3 \end{gathered}`

To get FR:

`\begin{gathered} FR=YS-1 \\ FR=3-1 \\ FR=2 \end{gathered}`

Therefore, the lengths of the medians are:

`\begin{gathered} YS=3 \\ FR=2 \end{gathered}`