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

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

Options:

  1. 1 cm to 17 cm
  2. 6 cm to 16 cm
  3. 7 cm to 12 cm
  4. 5 cm to 12 cm

Correct Answer: 6 cm to 16 cm

Solution: 

The length of the third side must be greater than the difference of the other two sides and less than their sum: |5 - 12| < third side < 5 + 12, which gives 7 cm < third side < 17 cm.

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

Practice Questions

Q1
If the lengths of two sides of a triangle are 5 cm and 12 cm, what is the range of possible lengths for the third side?
  1. 1 cm to 17 cm
  2. 6 cm to 16 cm
  3. 7 cm to 12 cm
  4. 5 cm to 12 cm

Questions & Step-by-Step Solutions

If the lengths of two sides of a triangle are 5 cm and 12 cm, what is the range of possible lengths for the third side?
  • Step 1: Identify the lengths of the two sides of the triangle. Here, they are 5 cm and 12 cm.
  • Step 2: Calculate the difference between the two sides. This is |5 - 12| = 7 cm.
  • Step 3: Calculate the sum of the two sides. This is 5 + 12 = 17 cm.
  • Step 4: The length of the third side must be greater than the difference (7 cm) and less than the sum (17 cm).
  • Step 5: Write the range for the third side: 7 cm < third side < 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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