Question

in triangle qrs, qr = 8 and rs = 5. which expresses all possible lengths of side qs? qs = 13 5 < qs < 8 qs > 13 3 < qs < 13

Explanation:

Step1: Apply triangle - side inequality

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, $QSQR - RS$.

Step2: Calculate the upper - bound

Given $QR = 8$ and $RS = 5$, then $QR+RS=8 + 5=13$, so $QS<13$.

Step3: Calculate the lower - bound

$QR - RS=8 - 5 = 3$, so $QS>3$.

Answer:

D. $3 < QS < 13$