Question

5, 7, and x are the lengths of the sides of a triangle. Find the range of values of x.
[1 mark]

Answer 1

Using the triangle inequality theorem for the above triangle:
x + 5 > 7 ⟹ x > 2
[0.5 marks]

x + 7 > 5 ⟹ x > -2 (not valid because length of sides must be positive)
7 + 5 > x ⟹ x < 12

Combining the two valid statements:
2 < x < 12
[0.5 marks]