Question

The sum of the lengths of any two

sides of a triangle is greater than the
length of the third side. Write three
inequalities that represent the possible
values of x. Your friend claims the
value of x can be 1.5. Is your friend
correct? Explain.
7.3
5.5
X

Answer 1

• 1.8 < x < 12.8
• x cannot be 1.5

Explanation:

Given that the triangle inequality requires any two sides of a triangle together have a length greater than the third side, you want an inequality that defines the range of x.

Triangle inequality

For any assignment of sides a, b, c in a triangle, we require a+b > c.

Application

For any of the given lengths being the third side, the inequalities are ...

• 7.3 +5.5 > x ⇒ x < 12.8
• 5.5 +x > 7.3 ⇒ 1.8 < x
• x +7.3 > 5.5 ⇒ -1.3 < x

All of these must be satisfied, so we must have ...

1.8 < x < 12.8

Claim

Your friend claims 1.5 is a possible third side length. The above inequality excludes that value from consideration

1.5 is not a possible value of x.