Question

If TU = w - 42 and SV = w - 67, what is the value of w?

Answer 1

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

$SV=\frac{1}{2}TU$

So,

$\begin{gathered} w-67=\frac{1}{2}(w-42) \\ w-\frac{w}{2}=67-21 \\ \frac{w}{2}=46 \\ w=92 \end{gathered}$

Hence, value of w is 92.