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In a triangle, if the lengths of two sides are 7 cm and 10 cm, what could be the

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Question: In a triangle, if the lengths of two sides are 7 cm and 10 cm, what could be the maximum 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 sum of the lengths of any two sides must be greater than the length of the third side. Therefore, the maximum length of the third side can be 16 cm (7 + 10 - 1). Hence, the answer is 17 cm.

In a triangle, if the lengths of two sides are 7 cm and 10 cm, what could be the

Practice Questions

Q1
In a triangle, if the lengths of two sides are 7 cm and 10 cm, what could be the maximum length of the third side?
  1. 16 cm
  2. 17 cm
  3. 18 cm
  4. 19 cm

Questions & Step-by-Step Solutions

In a triangle, if the lengths of two sides are 7 cm and 10 cm, what could be the maximum length of the third side?
  • Step 1: Understand that in a triangle, the lengths of any two sides must be greater than the length of the third side.
  • Step 2: Identify the lengths of the two sides given in the problem, which are 7 cm and 10 cm.
  • Step 3: Use the triangle inequality theorem to find the maximum length of the third side. The theorem states that the sum of the lengths of any two sides must be greater than the length of the third side.
  • Step 4: Calculate the maximum possible length of the third side by adding the lengths of the two sides: 7 cm + 10 cm = 17 cm.
  • Step 5: Since the maximum length of the third side must be less than the sum of the other two sides, the maximum length of the third side can be 16 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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