Answer:
No, a triangle with sides 11, 14, 17 is not a right triangle.
Explanation:
If this were a right triangle, the 11 and 14 would be the legs and the 17 would be the hypotenuse AND Pythagorean Theorem would work.
Check it:
a^2 + b^2 = c^2
11^2 + 14^2 =? 17^2
121 + 196 = 289 ?
317 = 289 ? Nope.
Pythagorean thm doesn't work on this triangle, so it is not a right triangle.