A triangle has two sides of length 7 and 1. What is the largest possible whole-number length for the third side?
Question
A triangle has two sides of length 7 and 1. What is the largest possible whole-number length for the third side?
Solution
The length of the third side of a triangle must be less than the sum of the lengths of the other two sides, according to the triangle inequality theorem.
So, the third side must be less than 7 + 1 = 8.
However, since the question asks for the largest possible whole number length for the third side, we need to subtract 1 from 8 (because the third side must be less than 8, not equal to 8).
Therefore, the largest possible whole-number length for the third side of the triangle is 7.
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