The sides of a triangle are 7, 4, n. If n is an integer, state the largest and smallest possible values of n.smallest value-largest value-plz help
Accepted Solution
A:
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.