If two sides of a triangle are 7 cm and 10 cm, what is the range of possible len

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What’s inside this PDF?

Question: If two sides of a triangle are 7 cm and 10 cm, what is the range of possible lengths for the third side?

Options:

3 cm to 17 cm
4 cm to 16 cm
5 cm to 15 cm
6 cm to 13 cm

Correct Answer: 3 cm to 17 cm

Solution:

By the triangle inequality theorem, the length of the third side must be greater than the difference of the other two sides and less than their sum: |7 - 10| < x < 7 + 10, which gives 3 < x < 17.

If two sides of a triangle are 7 cm and 10 cm, what is the range of possible len

Practice Questions

If two sides of a triangle are 7 cm and 10 cm, what is the range of possible lengths for the third side?

3 cm to 17 cm
4 cm to 16 cm
5 cm to 15 cm
6 cm to 13 cm

Questions & Step-by-Step Solutions

If two sides of a triangle are 7 cm and 10 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 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 difference of the two sides: 10 cm - 7 cm = 3 cm.
Step 4: Calculate the sum of the two sides: 10 cm + 7 cm = 17 cm.
Step 5: Write the inequality based on the triangle inequality theorem: 3 cm < x < 17 cm.
Step 6: This means the length of the third side (x) 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.

If two sides of a triangle are 7 cm and 10 cm, what is the range of possible len

What’s inside this PDF?

If two sides of a triangle are 7 cm and 10 cm, what is the range of possible len

Practice Questions

Questions & Step-by-Step Solutions

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