Which one of the following triplets can be measures of the sides of a triangle?

For any triangle with sides a, b, and c, the following conditions must be satisfied: 

a + b > c 

b + c > a

c + a > b

We need to check each triplet to see if it satisfies the triangle inequality theorem.

Option A: 1, 2, 4

1 + 2 = 3 $$\not>$$​ 4 The sum of 1 and 2 is not greater than 4, so this triplet cannot form a triangle.

Option B: 11, 3, 7

11 + 3 = 14 > 7

13 + 7 = 10 $$\not>$$​ 11 The sum of 3 and 7 is not greater than 11, so this triplet cannot form a triangle.

Option C: 1, 15, 3

1 + 15 = 16 > 3

1 + 3 = 4 $$\not>$$​ 15 The sum of 1 and 3 is not greater than 15, so this triplet cannot form a triangle.

Option D: 5, 7, 4

5 + 7 = 12 > 4

7 + 4 = 11 > 5

4 + 5 = 9 > 7 All conditions are satisfied, so this triplet can form a triangle.

Thus, The correct triplet is D (5, 7, 4)