Given segment dividing triangle at two points of a sides of a triangle. Also, RS=RT and RV=VU.
We know midsegment theorem,
THE MIDSEGMENT THEOREM:
In triangle RTU, if RS=RT and RV=VU then TU parallel SV and
[tex]SV=\frac{1}{2}TU[/tex]
So,
[tex]\begin{gathered} w-67=\frac{1}{2}(w-42) \\ w-\frac{w}{2}=67-21 \\ \frac{w}{2}=46 \\ w=92 \end{gathered}[/tex]
Hence, value of w is 92.
