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).
Last updated on May 28, 2025
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