Worksheet: Inequality in One Triangle: Sides

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 𝐴𝐢 lie?

  • A ( 3 . 3 , 3 5 . 3 ]
  • B [ 3 . 3 , 3 5 . 3 ]
  • C ( 3 . 3 , 3 5 . 3 )
  • D [ 3 . 3 , 3 5 . 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?

  • A 5 , 3 , 8
  • B 5 , 2 , 8
  • C 2 , 5 , 6

Q4:

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

  • A 1 8 , 1 2 , 6
  • B 3 , 1 2 , 1 1
  • C 1 3 , 6 , 1 5
  • D 6 , 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?

  • A 7 cm, 36 cm, and 43 cm
  • B 13 cm, 18 cm, and 43 cm
  • C 13 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 , 1 2 )
  • B ( 3 , 9 )
  • C ( βˆ’ 6 , 1 2 )
  • D [ 6 , 1 2 ]

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:

Determine whether the following sentence is 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 π‘₯ if (π‘₯+6) cm, 2 cm, and 25 cm represent the lengths of the sides of a triangle.

  • A 2 < π‘₯ < 2 1
  • B 2 9 < π‘₯ < 3 3
  • C 1 7 < π‘₯ < 2 5
  • D 2 3 < π‘₯ < 2 7
  • E 1 7 < π‘₯ < 2 1

Q13:

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

  • A 19 cm, 1 cm, 8 cm
  • B 4 cm, 18 cm, 3 cm
  • C 11 cm, 11 cm, 4 cm
  • D 18 cm, 7 cm, 5 cm

Q14:

Is the following statement true or false: β€œThe 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 𝐴𝐡𝐢, is 𝐴𝐡+π΅πΆβˆ’π΄πΆ<, =, 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:

𝐴 𝐡 𝐢 is a triangle where 𝐹 is the midpoint of 𝐡𝐢. Is 𝐴𝐡+𝐴𝐢<, =, or >𝐴𝐹+𝐡𝐹?

  • 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 .

  • A 4.1 cm, 7.8 cm
  • B 4.7 cm, 10.9 cm
  • C 3.7 cm, 11.9 cm
  • D 2.7 cm, 12.9 cm

Q22:

𝐴 𝐡 𝐢 is a triangle where (𝐴𝐡)>(𝐴𝐢)+(𝐡𝐢), 𝐴𝐡=5.1cm, 𝐴𝐢=2.6cm, οƒ«π΄π·βŸ‚βƒ–οƒ©οƒ©οƒ©οƒ©βƒ—π΅πΆ at the point 𝐷, and 𝐴𝐷=2.4cm. Calculate the length of 𝐡𝐢.

Q23:

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

  • A π‘₯ > 1 0
  • B π‘₯ > βˆ’ 6
  • C π‘₯ < βˆ’ 1 8
  • D 2 0 < π‘₯ < 2 2
  • E 8 < π‘₯ < 1 4

Q24:

A triangle has sides of lengths 5 cm, 8 cm, and π‘₯ cm. State the range of values that π‘₯ could take.

  • A π‘₯ > 3
  • B π‘₯ = √ 8 9
  • C π‘₯ < 1 3
  • D √ 3 9 < π‘₯ < √ 8 9
  • E 3 < π‘₯ < 1 3

Q25:

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

  • A 2 , 5 , 7
  • B 2 , 5 , 8
  • C 5 , 3 , 6

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