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In a triangle, if the lengths of two sides are 7 cm and 10 cm, which of the foll

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Question: In a triangle, if the lengths of two sides are 7 cm and 10 cm, which of the following could be the length of the third side?

Options:

  1. 3 cm
  2. 15 cm
  3. 5 cm
  4. 17 cm

Correct Answer: 3 cm

Solution: 

According to the triangle inequality theorem, the length of the third side must be less than the sum and greater than the difference of the other two sides. Therefore, the third side must be greater than 3 cm and less than 17 cm.

In a triangle, if the lengths of two sides are 7 cm and 10 cm, which of the foll

Practice Questions

Q1
In a triangle, if the lengths of two sides are 7 cm and 10 cm, which of the following could be the length of the third side?
  1. 3 cm
  2. 15 cm
  3. 5 cm
  4. 17 cm

Questions & Step-by-Step Solutions

In a triangle, if the lengths of two sides are 7 cm and 10 cm, which of the following could be the length of the third side?
  • Step 1: Identify the lengths of the two sides of the triangle. Here, they are 7 cm and 10 cm.
  • Step 2: Use the triangle inequality theorem, which states that the length of any side of a triangle must be less than the sum of the other two sides and greater than the difference of the other two sides.
  • Step 3: Calculate the sum of the two sides: 7 cm + 10 cm = 17 cm. This means the third side must be less than 17 cm.
  • Step 4: Calculate the difference of the two sides: 10 cm - 7 cm = 3 cm. This means the third side must be greater than 3 cm.
  • Step 5: Combine the results from Steps 3 and 4. The length of the third side must be greater than 3 cm and less than 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, and the difference of the lengths of any two sides must be less than the length of the third side.
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