Can three lengths make a triangle?

Answer Key - Grade 8 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Bo lays out three pieces of yarn: 2.5 cm, 5.5 cm and 4 cm. The sketch adds the two shorter ones. Can the three make a triangle?

   • No: a triangle needs three equal sides to close up
   • No: 5.5 cm is longer than 2.5 cm
   • Yes: 2.5 + 4 = 6.5 cm, longer than 5.5 cm
2. 2.

   Esme lays out three crayons: 7 cm, 11 cm and 4 cm. The sketch adds the two shorter ones. Can the three make a triangle?

   • No: 4 + 7 = 11 cm exactly, so they lie flat
   • Yes: any three crayons make a triangle, whatever the lengths
   • Yes: 11 + 4 = 15 cm, longer than 7 cm
   • Yes: 4 + 7 is not shorter than 11 cm
3. 3.

   Jun lays out three paper strips: 8 cm, 3.5 cm and 4.5 cm. The sketch adds the two shorter ones. Can the three make a triangle?

   • Yes: 8 + 3.5 = 11.5 cm, longer than 4.5 cm
   • Yes: 3.5 + 4.5 is not shorter than 8 cm
   • No: 3.5 + 4.5 = 8 cm exactly, so they lie flat
   • Yes: any three paper strips make a triangle
4. 4.

   Kira hinges two paper strips, 5 cm and 11 cm, as two sides of a triangle. The third side is more than ? cm and less than ? cm. Type both numbers, smaller first.

   6, 16
5. 5.

   Luz hinges two pieces of yarn, 6 cm and 13 cm, as two sides of a triangle. The third side is more than ? cm and less than ? cm. Type both numbers, smaller first.

   7, 19
6. 6.

   Labeled sketch, not to scale: the 8 cm and 12 cm pencils are joined at one end like a hinge. Milo hinges two pencils, 8 cm and 12 cm, as two sides of a triangle. The third side is more than ? cm and less than ? cm. Type both numbers, smaller first.

   4, 20
7. 7.

   Noah hinges two paper strips, 7 cm and 15 cm, as two sides of a triangle. The third side is more than ? cm and less than ? cm. Type both numbers, smaller first.

   8, 22
8. 8.

   Pia has 6 cm and 10 cm paper strips for two sides of a triangle. The sketch shows the hinge. Which length can the third side be?

   • 2 cm
   • 9 cm
   • 4 cm
   • 18 cm
9. 9.

   Ren has 5 cm and 8 cm crayons for two sides of a triangle. The sketch shows the hinge. Which length can the third side be?

   • 15 cm
   • 7 cm
   • 13 cm
   • 2 cm
10. 10.

    Zee has 3 cm and 11 cm paper strips for two sides of a triangle. The sketch shows the hinge. Which length can the third side be?

    • 16 cm
    • 8 cm
    • 12 cm
    • 6 cm