Question

The set (3,5,___________ could not be the sides of a triangle 3,2,5,7

Answer 1

Answer:

  (3, 5, 2)

Step-by-step explanation:

Many authors interpret the triangle inequality to mean the sum of the two short sides must exceed the length of the long side. For side measures 2, 3, 5, the sum of the two short sides is exactly equal to the long side, in violation of the triangle inequality. Hence (3, 5, 2) is not a triangle.

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Comment on the triangle inequality

Other authors allow the "or equal to" case, meaning sides of lengths 2, 3, 5 will be considered to be a triangle because 2+3=5. This interpretation of the triangle inequality will result in no solution to your question.

A (3, 5, 2) "triangle" will look like a line segment of length 5. It will have an area of zero.