Question

4,7 and a are the measure of sides of a triangle. Find the range of values of a.

• A. $3<s<11$
• B. $3<s<8$
• C. $3<s\le 7$
• D. $3\le s<7$

Answer 1

The correct option is A $3<s<11$

Using the triangle inequality theorem for the above triangle:
s+4 > 7 $⟹$ s > 3
s+7 > 3 $⟹$ s > -3 (not valid because length of sides must be positive)
7+4 > s $⟹$ s < 11

combining the two valid statements:
3 < s < 11