Chapter 6.4, Problem 10WE

To determine

To find: the longest side in $\Delta DFE$

Answer to Problem 10WE

DF is the longest side

Explanation of Solution

Formula used:In any triangle, the side opposite to the larger (greater) angle is longer

Calculation:

  

First find $\angle D,\angle E,\angle F$

According to angle sum property of a triangle, sum of all the angles of a triangle is $180°$

In $\Delta DFE$ ,

  $\begin{array}{l}\angle D=k°\\ \angle E=\left(k+2\right)°\\ \angle F=60°\end{array}$

So,

  $\begin{array}{l}\angle D+\angle E+\angle F=180°\\ \Rightarrow k°+\left(k+2\right)°+60°=180°\\ \Rightarrow 2k°+62°=180°\\ \Rightarrow 2k°=180°-62°=118°\\ \Rightarrow 2k°=118°\\ \Rightarrow k°=\frac{118°}{2}=59°\end{array}$

Therefore,

  $\begin{array}{l}\angle D=59°\\ \angle E=\left(59+2\right)°=61°\\ \angle F=60°\end{array}$

Compare all the angles

  $\angle D<\angle F<\angle E$

In any triangle, the side opposite to the larger (greater) angle is longer

So,

DF is the longest side