Integer length in a triangle
Geometry
Level
1
Two legs of a triangle have lengths of 7.4 and 17.3 respectively. Given that the length of the third side is a whole number, what is the largest possible length for the third side?
The answer is 24.
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The triangle inequality tells us that the third side is at most 7 . 4 + 1 7 . 3 = 2 4 . 7 . Since we are given that the length is integer, it is at most 2 4 .
Conversely, a triangle with side lengths of 7 . 4 , 1 7 . 3 , 2 4 exists, hence the maximum length is 24.