If a triangle has two sides of lengths 6 and 8, what is the maximum possible len

If a triangle has two sides of lengths 6 and 8, what is the maximum possible length of the third side?

If a triangle has two sides of lengths 6 and 8, what is the maximum possible length of the third side?

Step 1: Identify the lengths of the two sides of the triangle. Here, they are 6 and 8.
Step 2: To find the maximum possible length of the third side, remember the triangle inequality rule. This rule states that the length of any side of a triangle must be less than the sum of the other two sides.
Step 3: Calculate the sum of the two sides: 6 + 8 = 14.
Step 4: The maximum length of the third side must be less than this sum, so it can be at most 14 - 1 = 13 (we subtract 1 to ensure it's less than the sum).
Step 5: Now, apply the second part of the triangle inequality rule, which states that the length of the third side must also be greater than the difference of the two sides.
Step 6: Calculate the difference of the two sides: 8 - 6 = 2.
Step 7: Therefore, the third side must be greater than 2.
Step 8: The maximum possible length of the third side is the smaller value between 13 and the sum of the two sides minus 1, which is 13, and it must also be greater than 2.
Step 9: Thus, the maximum possible length of the third side is 13.

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.
Maximum Length of a Side – To find the maximum possible length of a side, it must be less than the sum of the other two sides.