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If the lengths of two sides of a triangle are 8 cm and 6 cm, what is the range o

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Question: If the lengths of two sides of a triangle are 8 cm and 6 cm, what is the range of possible lengths for the third side?

Options:

  1. 2 cm to 14 cm
  2. 2 cm to 10 cm
  3. 4 cm to 14 cm
  4. 4 cm to 10 cm

Correct Answer: 2 cm to 10 cm

Solution: 

The length of the third side must be greater than the difference of the other two sides and less than their sum: |8 - 6| < third side < 8 + 6, which gives 2 < third side < 14.

If the lengths of two sides of a triangle are 8 cm and 6 cm, what is the range o

Practice Questions

Q1
If the lengths of two sides of a triangle are 8 cm and 6 cm, what is the range of possible lengths for the third side?
  1. 2 cm to 14 cm
  2. 2 cm to 10 cm
  3. 4 cm to 14 cm
  4. 4 cm to 10 cm

Questions & Step-by-Step Solutions

If the lengths of two sides of a triangle are 8 cm and 6 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 8 cm and 6 cm.
  • Step 2: Calculate the difference between the two sides. This is |8 - 6| = 2 cm.
  • Step 3: Calculate the sum of the two sides. This is 8 + 6 = 14 cm.
  • Step 4: The length of the third side must be greater than the difference (2 cm) and less than the sum (14 cm).
  • Step 5: Write the inequality for the third side: 2 < third side < 14.
  • 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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