in triangle qrs, qr = 8 and rs = 5. which expresses all possible lengths of side qs?\nqs = 13\n5 < qs <…

Explanation:

Step1: Apply triangle - inequality theorem

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side, and the difference between the lengths of any two sides must be less than the length of the third side. Let (a = QR = 8), (b = RS=5), and (c = QS). Then (|a - b|\lt c\lt a + b).

Step2: Calculate the lower - bound

Calculate (|a - b|): (|8 - 5|=3). So (3\lt QS).

Step3: Calculate the upper - bound

Calculate (a + b): (8 + 5 = 13). So (QS\lt13).

Answer:

(3\lt QS\lt13)