Lesson Worksheet: The Triangle Inequality Mathematics

In this worksheet, we will practice defining the triangle inequality and identifying whether the given side lengths are valid for constructing a triangle.


Complete the sentence: The sum of the lengths of any two sides in a triangle is the length of the other side.

  • Aless than
  • Bequal to
  • Cgreater than


Is it possible to form a triangle with side lengths 6 m, 7 m, and 18 m?

  • AThere is not enough information to tell.
  • BNo
  • CYes


Which of the following lists could be the lengths of sides of a triangle?

  • A5,3,8
  • B5,2,8
  • C2,5,6


Find the range of all possible values of 𝑥 if (𝑥+6) cm, 2 cm, and 25 cm represent the lengths of the sides of a triangle.

  • A2<𝑥<21
  • B29<𝑥<33
  • C17<𝑥<25
  • D23<𝑥<27
  • E17<𝑥<21


A triangle has sides of lengths 5 cm, 8 cm, and 𝑥 cm. State the range of values that 𝑥 could take.

  • A𝑥>3
  • B𝑥=89
  • C𝑥<13
  • D39<𝑥<89
  • E3<𝑥<13


What is the range of possible perimeters, 𝑃, of the given figure 𝐴𝐵𝐶𝐷𝐸 if 𝐴𝐶=5 and 𝐷𝐶=9?

  • A36<𝑃<56
  • B19<𝑃<23
  • C𝑃>18
  • D𝑃<56
  • E18<𝑃<28


The perimeter of a triangle is 128 cm and the length of one of the sides is 22 cm. Which of the following can be the lengths of the other two sides?

  • A41 cm, 65 cm
  • B64 cm, 42 cm
  • C60 cm, 46 cm
  • D66 cm, 40 cm


Is the length of any side in a triangle less than, equal to or greater than the sum of the length of the other two sides?

  • Aequal to
  • Bgreater than
  • Cless than


Which of the following lists of numbers is NOT the lengths of sides of a triangle?

  • A18,12,6
  • B3,12,11
  • C13,6,15
  • D6,2,5


Which of the following could be side lengths of a triangle?

  • A7 cm, 36 cm, and 43 cm
  • B13 cm, 18 cm, and 43 cm
  • C13 cm, 36 cm, and 43 cm

This lesson includes 12 additional questions and 117 additional question variations for subscribers.

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