Question

In triangle QRS, QR = 8 and RS = 5. Which expresses all possible length of side QS?
A) QS = 13
B) 5 < QS < 8
C) QS > 13
D) 3 < QS < 13

Answer 1

Obviously it's answer D) Why?

a) any side of a triangle is SMALLER than the SUM of the 2 others

b) any side of a triangle is GREATER than the DIFFERENCE of the 2 others

Hence D) 8-5 < QS < 8+5==>3 < QS < 13

Answer 2

The possible length of third side QS is

$3<QS<13$

Given :

In triangle QRS, QR = 8 and RS = 5.

We know that the sum of two sides of a triangle is greater than the third side

In triangle QRS

$QR+RS>SQ\\8+5>SQ\\QS<13\\\\RS+SQ>QR\\5+QS>8\\QS>8-5\\QS>3$

From the above two inequalities we can say that

$3<QS<13$

Learn more :  brainly.com/question/16947073