Question
Download Solution PDFIn a triangle ABC, AB = 6 cm, BC = 11 cm. How many integral values of AC can be possible?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
According to the triangle inequality theorem, we have:
AB + BC > AC
6 + 11 > AC
17 > AC
AC + AB > BC
AC + 6 > 11
AC > 5
AC + BC > AB
AC + 11 > 6
AC > -5 (We can ignore this inequality as the length of a side of a triangle cannot be negative.)
Combining the first two inequalities, we get:
17 > AC > 5
Therefore, AC can take integral values from 6 to 16 (both inclusive). Hence, the number of integral values of AC that are possible is 11 (i.e., 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16).
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