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Which of the following are the possible side lengths of a triangle?

A. x = 15.8 in, y = 21.3 in, z = 42.1 in
B. x = 20.8 in, y = 16.3 in, z = 42.1 in
C. x = 20.8 in, y = 21.3 in, z = 37.1 in
D. x = 20.8 in, y = 21.3 in, z = 47.1 in

Answer :

Answer:

C. x = 20.8 in, y = 21.3 in, z = 37.1 in

Step-by-step explanation:

We can find which sets of data are the possible side lengths of a triangle by this rule:

[tex]\boxed{|x-y| < z < |x+y|}[/tex]

where:

  • x and y are the shorter sides
  • z is the longest side

Option A.

Given the longest side (z) = 42.1 and:

  • [tex]|x-y|=|15.8-21.3|=5.5[/tex]
  • [tex]|x+y|=|15.8+21.3|=37.1[/tex]

Then Option A cannot be side lengths of a triangle since z > |x+y|.

Option B.

Given the longest side (z) = 42.1 and:

  • [tex]|x-y|=|20.8-16.3|=4.5[/tex]
  • [tex]|x+y|=|20.8+16.3|=37.1[/tex]

Then Option B cannot be side lengths of a triangle since z > |x+y|.

Option C.

Given the longest side (z) = 37.1 and:

  • [tex]|x-y|=|20.8-21.3|=0.5[/tex]
  • [tex]|x+y|=|20.8+21.3|=42.1[/tex]

Then Option C can be side lengths of a triangle since |x-y| < z < |x+y|.

Option D.

Given the longest side (z) = 47.1 and:

  • [tex]|x-y|=|20.8-21.3|=0.5[/tex]
  • [tex]|x+y|=|20.8+21.3|=42.1[/tex]

Then Option D cannot be side lengths of a triangle since z > |x+y|.

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