Triangle's Perimeter
Geometry
Level
3
If is a positive integer and are sides of a triangle, then what is its perimeter?
The answer is 5.
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1 solution
For the ( n − 2 ) ! to have meaning, it must be true that: n − 2 ≥ 2 ⇒ n ≥ 2
For the ( 2 − n ) ! to have meaning, it must be true that: 2 − n ≤ 2 ⇒ n ≤ 2
Therefore: n = 2
So, the perimeter is:
P = n ! + ( n − 2 ) ! + n ⋅ ( 2 − n ) ! = 2 ! + 0 ! + 2 ⋅ 0 ! = 2 + 1 + 2 = 5