Question

A triangle has sides 45, 4x and 2x−4. What is the possible range of x?

Answer 1

8 1/6 < x < 20.5.

Explanation:

Use the Triangle Inequality Theorem which states that the sum of any 2 sides of a triangle is always greater that the third side.

So for triangle to be formed:

4x + 2x - 4 > 45

6x > 49

x > 8 1/6.

Also 2x - 4 + 45 > 4x

41 > 2x

2x < 41

x < 20.5.