Answer:
11 > n > 4
Step-by-step explanation:
Given any two sides of a triangle, we now that the sum of such sides MUST be greater than the measure of the remaining side. This is, given the three sides a, b and c, it must be that:
a + b > c
a + c > b
b + c > a
For our case:
7 + 4 > n (1) ---> 11>n
7 + n > 4 (2)
4 + n > 7 (3)
The 1 inequality says that the n side MUST be less than 11.
Now, pick the (3) inequality and subtract 4 in both sides:
4 + n -4 > 7 - 4
n > 3
So, the n side must be grater than 3.
Thus, the solution is:
11 > n > 3
As we are working with integers we now that the grater integer larger than 3 is 4, and the greater integer less than 11 is 10. So, the side must be equal or greater to 4 and equal or less than 10:
10 >= n >= 4
