Question

consider the triangle shown. which shows the sides in order from longest to shortest? p 105° r 40° 35° q

Explanation:

Step1: Recall angle - side relationship

In a triangle, the longest side is opposite the largest angle and the shortest side is opposite the smallest angle.

Step2: Identify angle measures

The angles of the triangle are $\angle P = 105^{\circ}$, $\angle R=40^{\circ}$, $\angle Q = 35^{\circ}$.

Step3: Match sides to angles

The side opposite $\angle P$ is $\overline{RQ}$, the side opposite $\angle R$ is $\overline{PQ}$, and the side opposite $\angle Q$ is $\overline{RP}$.
Since $105^{\circ}>40^{\circ}>35^{\circ}$, the order of the sides from longest to shortest is $\overline{RQ},\overline{PQ},\overline{RP}$.

Answer:

$\overline{RQ},\overline{PQ},\overline{RP}$