According to the Triangle Inequality Theorem, the sum of the lengths of two sides of a triangle must be greater than the length of the 3rd side.
So, if a triangle has sides a, b, and c. Then,
a + b > c
a + c > b
b + c > a
To solve this question, let's test the options.
a) 4, 4, 4.
a = 4, b = 4, and c = 4.
a + b > c → 4 + 4 = 8; 8 > 4
a + c > b → 4 + 4 = 8; 8 > 4
b + c > a → 4 + 4 = 8; 8 > 4
So, it could be a triangle.
b) 3, 6, 9
a = 3, b = 6, and c = 9.
a + b > c → 3 + 6 = 9; 9 = 9.
So, it could not be a triangle.
c) 5, 5, 10
a = 5, b = 5, and c = 10.
a + b > c → 5 + 5 = 10; 10 = 10
So, it could not be a triangle.
d) 13, 5, 6
a = 13, b = 5, and c = 6.
a + b > c → 13 + 5 = 18; 18 > 6
a + c > b → 13 + 6 = 19; 19 > 5
b + c > a → 5 + 6 = 11; 11 < 13
So, it could not be a triangle.
Answer: A.