Question

3. In ΔABC, AB = 5 inches and BC = 3 inches. Which of the choices represents all possible values for AC, in inches?

Answer 1

2< AC<8

Explanation:

For a triangle to exits sum of two sides must always be greater than the the third side

⇒ AC< AB+ BC =5+3=8 in

⇒AC<8 in

Also, the difference of the two sides must be smaller than the length of third side

⇒ AC> | AB-BC| = |5-3| =2

AC> 2 in

therefore, we can say 2< AC<8. Hence, AC can takes 3,4,5,6 values