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If the lengths of two sides of a triangle are 5 cm and 12 cm, what is the maximu

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Question: If the lengths of two sides of a triangle are 5 cm and 12 cm, what is the maximum possible length of the third side?

Options:

  1. 16 cm
  2. 17 cm
  3. 18 cm
  4. 19 cm

Correct Answer: 17 cm

Solution: 

According to the triangle inequality theorem, the length of the third side must be less than the sum of the other two sides. Therefore, the maximum length is 5 + 12 = 17 cm.

If the lengths of two sides of a triangle are 5 cm and 12 cm, what is the maximu

Practice Questions

Q1
If the lengths of two sides of a triangle are 5 cm and 12 cm, what is the maximum possible length of the third side?
  1. 16 cm
  2. 17 cm
  3. 18 cm
  4. 19 cm

Questions & Step-by-Step Solutions

If the lengths of two sides of a triangle are 5 cm and 12 cm, what is the maximum possible length of the third side?
  • Step 1: Identify the lengths of the two sides of the triangle. In this case, they are 5 cm and 12 cm.
  • Step 2: Understand the triangle inequality theorem. This theorem states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides.
  • Step 3: Calculate the sum of the two known sides. Add 5 cm and 12 cm together: 5 + 12 = 17 cm.
  • Step 4: Conclude that the maximum possible length of the third side must be less than this sum. Therefore, the maximum length of the third side is 17 cm.
  • Triangle Inequality Theorem – The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
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