In a ΔABC, AB = 6 cm, BC = 11 cm. How many integral values of AC are possible?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 11.
According to the triangle inequality theorem,
AB + BC > AC
⇒ 6 + 11 > AC
⇒ 17 > AC
Also, AC + AB > BC
⇒ AC + 6 > 11
⇒ AC > 5
Also, AC + BC > AB
⇒ AC + 11 > 6
⇒ AC > -5 (Not Possible)
The number of possible values of AC is 11 (i.e., 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16)