Which of the following three lengths could not create a triangle?
A) 2, 3, 4   B) 3.5, 33.5, 66.5   C) 22, 2, 44   D) 1, 10, 100

Solution:

"Can any three lengths make up the triangle?" The answer to the above query is decided on the basis of the triangle inequality theorem.

Triangle inequality theorem: It states that the sum of any two sides of the triangle should be greater than the length of the third side.

Given, Option A) 2, 3, 4 - sum of 2 and 3 is greater than 4

Option B) 3.5, 33.5, 66.5 - sum of 3.5 and 33.5 is less than 66.5.

Option C) 22, 2, 44 - sum of 2 and 22 is less than 44.

Option D) 1, 10, 100 - sum of 1 and 10 is less than 100.

Thus, option A) is the only option where the triangle inequality theorem holds true.

Which of the following three lengths could not create a triangle? A) 2, 3, 4   B) 3.5, 33.5, 66.5   C) 22, 2, 44   D) 1, 10, 100

Summary:

Option A is the only option where the triangle inequality theorem holds true. Thus, options B, C, and D cannot form a triangle.