Chapter 6.4, Problem 11WE

To determine

To find:the longest side in the given figure.

Answer to Problem 11WE

  $WT$ is the longest side.

Explanation of Solution

Formula used:In a triangle, the side opposite to the larger angle is longer.

Calculation:

  

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

Find $\angle R$

In $\Delta RWS$ ,

  $\begin{array}{l}\angle R+\angle W+\angle S=180°\left\{\text{using}\text{angle}\text{sum}\text{property}\right\}\\ \Rightarrow \angle R+60°+60°=180°\\ \Rightarrow \angle R+120°=180°\\ \Rightarrow \angle R=180°-120°=60°\end{array}$

As $\angle R=\angle W=\angle S$ , RWS is an equilateral triangle

(in an equilateral triangle, all the angles are equal)

Therefore,

  $RW=WS=RS$ (as all the sides of an equilateral triangle are equal)

Now find $\angle T$

Consider $\Delta WTS$

Using angle sum property,

  $\begin{array}{l}\angle W+\angle T+\angle S=180°\\ \Rightarrow 54°+\angle T+65°=180°\\ \Rightarrow \angle T+119°=180°\\ \Rightarrow \angle T=180°-119°=61°\end{array}$

In a triangle, the side opposite to the larger angle is longer,

So,

  $ST<WS<WT$

Also, $RW=WS=RS$

So, $RW=WS=RS<WT$

Therefore, $WT$ is the longest side.