Chapter 1.5, Problem 19PSB

To determine

To-Determine: The value of VM.

Answer to Problem 19PSB

  $\overline{VM}=16$

Explanation of Solution

Given:

  

  $\begin{array}{l}\overleftrightarrow{TP}\text{bisects }\overline{VS}\text{and }\overline{MR}\\ \overline{VM}\cong \overline{SR}\\ MP=9,VT=6\\ \text{Perimeter of MRSV = 62}\end{array}$

Concept Used:

Bisector of a side divides into two equal parts.

Calculation:

Here, we have

  $\begin{array}{l}\overleftrightarrow{TP}\text{bisects }\overline{VS}\text{and }\overline{MR}\\ \overline{VM}\cong \overline{SR}\\ MP=9,VT=6\\ \text{Perimeter of MRSV = 62}\\ \because \text{ Perimeter of MRSV =}\overline{MR}+\overline{RS}+\overline{SV}+\overline{VM}\\ \Rightarrow 62=2\overline{MP}+2\overline{VM}+2\overline{VT}\\ \Rightarrow 31=\overline{MP}+\overline{VM}+\overline{VT}\\ \Rightarrow 31=9+\overline{VM}+6\\ \Rightarrow 16=\overline{VM}\\ \therefore \overline{VM}=16\end{array}$

Conclusion:

  $\overline{VM}=16$