Question

Which of the following are not the lengths of the sides of a triangle?

a) 2, 3, 4
b) 2, 3, 6
c) 2, 3, 3
d) 2, 3, 6

Answer 1

The lengths of the sides of a triangle must satisfy the triangle inequality theorem. Using the theorem, we can determine which sets of side lengths do not form a triangle.

Step-by-step explanation:

The lengths of the sides of a triangle must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let's apply this theorem to each set of side lengths:

a) 2, 3, 4: 2+3=5 is greater than 4, so this is a valid triangle.

b) 2, 3, 6: 2+3=5 is less than 6, so this is not a valid triangle.

c) 2, 3, 3: 2+3=5 is equal to 3, so this is not a valid triangle.

d) 2, 3, 6: 2+3=5 is less than 6, so this is not a valid triangle.

Therefore, the sides that are not lengths of a triangle are b) 2, 3, 6 and d) 2, 3, 6.