Respuesta :

The smallest value it could be is 4 and the largest value it could be is 10.

The triangle inequality theorem states that any two sides of a triangle must have a sum greater than the third side.  Given the two sides we have, 7 and 4, the sum would be 11; this would mean that the missing side could be no more than 10.

If we take the unknown side and the smallest one we're given, we would have the inequality 
n+4>7

Subtracting 4 from both sides we would have n>3.  That means it would have to be the next integer up, which would be 4.

Smallest value and largest value of n is [tex]11 , 3[/tex].

The third side of a triangle has a range,

[tex]Sum\; of \;two\; other\; sides\geq n\geq Difference\; of\; the\; sides[/tex]

[tex]7+4\geq n \geq7-4[/tex]

[tex]11\geq n \geq 3[/tex]

Therefore

Largest[tex]=11[/tex]

Smallest[tex]=3[/tex]

Learn more about Triangle here:

https://brainly.com/question/17893810?referrer=searchResults

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