Question

Find all possible values of x if these represent side of a triangle 2x,5-x,4

Answer 1

• -1/3 < x < 3 or x = (-1/3, 3)

Explanation:

Given sides of a triangle:

• 2x, 5 - x, 4

Triangle inequality theorem:

• Any side is smaller than the some of the other two.

Apply to the given triangle:

• 2x + 5 - x > 4 ⇒ x > -1
• 2x + 4 > 5 - x ⇒ 3x > -1 ⇒ x > -1/3
• 5 - x + 4 > 2x ⇒ 3x < 9 ⇒ x < 3

Combine all the inequalities:

• -1/3 < x < 3
• x = (-1/3, 3)