Chapter 7.6, Problem 29WE

To determine

To Explain : If any triangle exists satisfying the give condition.

Explanation of Solution

Given information:

  $\text{Δ}ROS\text{in which the trisections of}\angle O\text{intersect}\overline{RS}\text{at}D\text{and}E$

  $\begin{array}{cc}RD& =1\\ DE& =2\\ ES& =4\end{array}$

Here consider the diagram below:

  

Further, this is a fact that if this is triangle, then trisections of angle will not trisect the opposite side.

Therefore, if $\text{Δ}ROS$ . is a triangle and $OD$ and $OE$ trisect $\angle O$ then:

  $RD\ne DE\ne ES$

Here,

  $\begin{array}{l}RD=1\\ DE=2\\ ES=4\end{array}$

Therefore, the condition is fulfilled.

Hence, this is possible.