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jmc

geometry junior

Problem

A triangle has sides of length 5 and 6 units. The length of the third side is units, where is an integer. What is the largest possible perimeter of the triangle?
Solution
If a triangle has sides of length 5 and 6 units, that means the third side must be smaller than 11 units. Since the third side is also an integer length, that means the third side can be at most 10 units. Verifying that 5 units, 6 units, and 10 units do make a valid triangle, we can see that the largest possible perimeter is
Final answer
21\text{ units}