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 is-largest value is-

Answer:11 > n > 4Step-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 > ca + c > bb + c > aFor our case:7 + 4 > n (1) ---> 11>n7 + 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 - 4n > 3So, the n side must be grater than 3. Thus, the solution is:11 > n > 3As 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