Question

A triangle has two sides of lengths 4 and 5? What is the value of the third side?

Answer 1

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side.
You can write this as a formula: A + B > x, where x is the third side.

A + B > x
4 + 5 > x
9 > x or x < 9

A + x > B
4 + x > 5
x > 1

B + x > A
5 + x > 4
x > -1

Given two side lengths 4 and 5, the third side must be between 1 and 9.

Answer 2

It would be 20 given the formula A=BH.