Question

The lengths of two sides of a triangle are 5 and 14. Find the lengths that the third side must be greater than and less than.

Answer 1

The third side of the triangle must be greater than 4 and less than 19. This follows from the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side, and the difference between any two sides of a triangle must be less than the third side. Therefore, the third side must be greater than 4 (5 + 4) and less than 19 (14 - 4).