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Which of the following can be the lengths of the sides of a triangle?

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Question: Which of the following can be the lengths of the sides of a triangle?

Options:

  1. 2, 3, 5
  2. 4, 4, 8
  3. 5, 5, 10
  4. 6, 8, 10

Correct Answer: 6, 8, 10

Solution: 

The triangle inequality theorem states that the sum of the lengths of any two sides must be greater than the length of the third side. Only 6, 8, and 10 satisfy this condition.

Which of the following can be the lengths of the sides of a triangle?

Practice Questions

Q1
Which of the following can be the lengths of the sides of a triangle?
  1. 2, 3, 5
  2. 4, 4, 8
  3. 5, 5, 10
  4. 6, 8, 10

Questions & Step-by-Step Solutions

Which of the following can be the lengths of the sides of a triangle?
  • Step 1: Understand that a triangle has three sides.
  • Step 2: Remember the triangle inequality theorem. It says that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
  • Step 3: Let's say we have three lengths: 6, 8, and 10. We need to check if they can form a triangle.
  • Step 4: Check the first condition: 6 + 8 > 10. This is true because 14 > 10.
  • Step 5: Check the second condition: 6 + 10 > 8. This is also true because 16 > 8.
  • Step 6: Check the third condition: 8 + 10 > 6. This is true because 18 > 6.
  • Step 7: Since all three conditions are satisfied, the lengths 6, 8, and 10 can form a triangle.
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