If you have a triangle with sides a, b and c, then:
[tex] a+b>c,\\a+c>b,\\b+c>a. [/tex]
In your case let a=4 in, b=12 in annd c=17 in. Check these three inequalities:
1. 4+12=16 is less than 17 - inequality a+b>c doesn't hold.
2. 4+17>12 - inequality a+c>b holds.
3. 12+17>4 - inequality b+c>a holds.
Since only two from three inequalities are true, then the triangle doesn't exist.
Answer: correct choice is D - This triangle does not exist because the sum of 4 and 12 is less than 17.
