Question

5. The sides of a triangle are 5, 12, and n. Write an inequality that expresses the interval of values

that n may have.
05 05 07 07 4

Answer 1

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Using this fact, we can write:

5 + 12 > n

and

5 + n > 12

and

12 + n > 5

Simplifying these inequalities, we get:

17 > n

and

n > -7

and

n > -5

Therefore, the interval of values that n may have is -7 < n < 17.