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Which of the following does not represent the lengths of the sides of a triangle?
A. 2 cm, 6 cm, 7 cm
B. 5 cm, 5 cm, 8 cm
C. 5 cm, 2 cm, 5 cm
D. 3 cm, 10 cm, 15 cm​

Sagot :

Zhengliidn

I. Which of the following does not represent the lengths of the sides of a triangle?

Formula to be used:

  • a + b > c
  • a + c > b
  • b + c > a

Checking for Letter A (2 cm, 6 cm, 7 cm)

  • [tex]\large\tt {2\:+\:6 > 7}[/tex]
  • [tex]\large \tt {8 \: > 7\:=True}[/tex]

  • [tex]\large\tt {2\:+\:7 > 6}[/tex]
  • [tex]\large \tt {9 \: > 6\:=True}[/tex]

  • [tex]\large\tt {6\:+\:7 > 2}[/tex]
  • [tex]\large \tt {13 \: > 2\:=True}[/tex]

∵ The sum of any two lengths is greater than the third length. As a result, Letter A represents the length of a triangle's sides.

Checking for Letter B (5 cm, 5 cm, 8 cm)

  • [tex]\large\tt {5\:+\:5 > 8}[/tex]
  • [tex]\large \tt {10 \: > 8\:=True}[/tex]

  • [tex]\large\tt {5\:+\:8 > 5}[/tex]
  • [tex]\large \tt {13 \: > 5\:=True}[/tex]

  • [tex]\large\tt {5\:+\:8 > 5}[/tex]
  • [tex]\large \tt {13 \: > 5\:=True}[/tex]

∵ The sum of any two lengths is greater than the third length. As a result, Letter B represents the length of a triangle's sides.

Checking for Letter C (5 cm, 2 cm, 5 cm)

  • [tex]\large\tt {5\:+\:2 > 5}[/tex]
  • [tex]\large \tt {7 \: > 5\:=True}[/tex]

  • [tex]\large\tt {5\:+\:5 > 2}[/tex]
  • [tex]\large \tt {10 \: > 2\:=True}[/tex]

  • [tex]\large\tt {2\:+\:5 > 5}[/tex]
  • [tex]\large \tt {7 \: > 5\:=True}[/tex]

∵ The sum of any two lengths is greater than the third length. As a result, Letter C represents the length of a triangle's sides.

Checking for Letter D (3 cm, 10 cm, 15 cm​)

  • [tex]\large\tt {3\:+\:10 > 15}[/tex]
  • [tex]\large \tt {13 \: > 15\:=False}[/tex]

  • [tex]\large\tt {3\:+\:15 > 10}[/tex]
  • [tex]\large \tt {18 \: > 10\:=True}[/tex]

  • [tex]\large\tt {10\:+\:15 > 3}[/tex]
  • [tex]\large \tt {25 \: > 3\:=True}[/tex]

∵ Since one of the solutions is false, the letter D does not represent the length of the sides of a triangle. (Letter D is the answer)

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