In any triangle, the length of the longest side (call it c) is no larger than the sum of the lengths of the smaller sides (call them a and b). We fittingly call this the triangle inequality,

a + b ≥ c

From the given choices, the correct one is the one in which the two smaller integers have a sum that's bigger than the largest integer. In this case, the third triplet cannot form the sides of a triangle.

{7, 20, 26} : 7 + 20 = 27 ≥ 26

{10, 19, 26} : 10 + 19 = 29 ≥ 26

{14, 25, 40} : 14 + 25 = 39 < 40

{14, 27, 38} : 14 + 27 = 41 ≥ 38