If the lengths of two sides of a triangle are 8 cm and 15 cm, what is the maximu

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Question: If the lengths of two sides of a triangle are 8 cm and 15 cm, what is the maximum possible length of the third side? (2021)

Options:

Correct Answer: 22 cm

Exam Year: 2021

Solution:

The maximum length of the third side is less than the sum of the other two sides, so it can be 22 cm.

If the lengths of two sides of a triangle are 8 cm and 15 cm, what is the maximum possible length of the third side? (2021)

If the lengths of two sides of a triangle are 8 cm and 15 cm, what is the maximum possible length of the third side? (2021)

Step 1: Identify the lengths of the two sides of the triangle. They are 8 cm and 15 cm.
Step 2: Understand that in a triangle, the length of any one side must be less than the sum of the lengths of the other two sides.
Step 3: Calculate the sum of the two known sides: 8 cm + 15 cm = 23 cm.
Step 4: The maximum possible length of the third side must be less than this sum, so it must be less than 23 cm.
Step 5: The maximum possible length of the third side is therefore 22 cm.

Triangle Inequality Theorem – The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.