Answer :
Answer:
[tex]3<QS<13[/tex]
Step-by-step explanation:
We have been given that in triangle QRS, [tex]QR=8[/tex] and [tex]RS=5[/tex]. We are asked to find the possible lengths of side QS.
We will use triangle inequality theorem to solve for QS.
Triangle inequality theorem states that sum of two sides of triangle must be greater than third side.
[tex]QS+RS>QR[/tex]
[tex]QS+5>8[/tex]
[tex]QS+5-5>8-5[/tex]
[tex]QS>3[/tex]
[tex]QS<RS+QR[/tex]
[tex]QS<5+8[/tex]
[tex]QS<13[/tex]
Upon combining both solutions, we will get:
[tex]3<QS<13[/tex]
Therefore, the solution [tex]3<QS<13[/tex] expresses all possible lengths of side QS.