Lesson Worksheet: Inequality in One Triangle: Sides Mathematics

In this worksheet, we will practice applying the triangle inequality to determine whether three given lengths can be sides of a triangle.

Q1:

In what interval must the length of 𝐴𝐶 lie?

  • A(3.3,35.3]
  • B[3.3,35.3]
  • C(3.3,35.3)
  • D[3.3,35.3)

Q2:

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

Q3:

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

  • A5,3,8
  • B5,2,8
  • C2,5,6

Q4:

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

Q5:

Two sides in a triangle have lengths 2.6 and 2.4. In what interval must the length of the third side be?

  • A(0,5)
  • B(2,2)
  • C(0.2,5)
  • D[0.2,5]

Q6:

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

Q7:

If the lengths of two sides of a triangle are 3 cm and 9 cm, determine the smallest interval to which the length of the third side belongs.

  • A(6,12)
  • B(3,9)
  • C(−6,12)
  • D[6,12]

Q8:

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

Q9:

Is it possible to form a triangle with side lengths 3 inches, 5 inches, and 7 inches?

  • AYes
  • BNo
  • CThere is not enough information to tell.

Q10:

True or False: Knowing the measures of the angles of a triangle is enough to be able to draw that triangle.

  • ATrue
  • BFalse

Q11:

If the measures of two sides of a triangle are 10 cm and 26 cm, which of the following could NOT be the measure of the third side?

  • A21 cm
  • B32 cm
  • C34 cm
  • D36 cm
  • E18 cm

Q12:

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

Q13:

Which of the following groups of lengths can form the sides of a triangle?

  • A19 cm, 1 cm, 8 cm
  • B4 cm, 18 cm, 3 cm
  • C11 cm, 11 cm, 4 cm
  • D18 cm, 7 cm, 5 cm

Q14:

True or False: The longest side of a triangle is opposite to the angle with the largest measure.

  • AFalse
  • BTrue

Q15:

Does the triangle with side lengths 8, 32, and 16 exist?

  • ANo
  • BYes

Q16:

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

Q17:

In triangle 𝐴𝐵𝐶, is 𝐴𝐵+𝐵𝐶−𝐴𝐶<, =, or >0?

  • A=
  • B<
  • C>

Q18:

Is it possible to draw a triangle with side lengths of 6 cm, 11 cm, and 9 cm?

  • AYes
  • BNo

Q19:

𝐴𝐵𝐶 is a triangle where 𝐹 is the midpoint of 𝐵𝐶. Is 𝐴𝐵+𝐴𝐶<, =, or >𝐴𝐹+𝐵𝐹?

  • A>
  • B=
  • C<

Q20:

If the measures of two sides of a triangle are 5 feet and 12 feet, what is the least possible whole-number measure for the third side?

Q21:

If the two side lengths of a triangle are 4.1 cm and 7.8 cm, then the length of the third is between and .

  • A4.1 cm, 7.8 cm
  • B4.7 cm, 10.9 cm
  • C3.7 cm, 11.9 cm
  • D2.7 cm, 12.9 cm

Q22:

𝐴𝐵𝐶 is a triangle where (𝐴𝐵)>(𝐴𝐶)+(𝐵𝐶), 𝐴𝐵=5.1cm, 𝐴𝐶=2.6cm, 𝐴𝐷⟂⃖⃗𝐵𝐶 at the point 𝐷, and 𝐴𝐷=2.4cm. Calculate the length of 𝐵𝐶.

Q23:

Write an inequality that describes all the values of 𝑥 such that a triangle with edge lengths (𝑥+8) cm, (𝑥+12) cm, and (𝑥+14) cm exists.

  • A𝑥>10
  • B𝑥>−6
  • C𝑥<−18
  • D20<𝑥<22
  • E8<𝑥<14

Q24:

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
  • D√39<𝑥<√89
  • E3<𝑥<13

Q25:

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

  • A2,5,7
  • B2,5,8
  • C5,3,6

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