Which of the following are possible side lengths of a triangle? (select all that apply) a. 1, 1, 2 b. 3, 4, 5 c. 5, 5, 11 d. 7, 8, 12 e. 4, 4, 4 f. 4, 8 ,13

Choice B

Choice D

Choice E

Explanation:

Use the triangle inequality theorem. This is the idea where adding any two sides must lead to a result larger than the third side; otherwise, a triangle is not possible. I recommend cutting out strings of paper of these lengths to confirm that you can make a triangle or not.

For choice A, a triangle is not possible since the first two sides add to 1+1 = 2, but this isn't larger than the third side of 2 units. All we can do really is just form a straight line and not a triangle. We can rule choice A out.

Choice B is a triangle. Specifically it is a 3-4-5 right triangle that is famous with the pythagorean theorem. Note how...

so adding any two sides of this triangle leads to the sum being larger than the third remaining side. Choice B is one of the answers.

Choice C is not a triangle. We have 5+5 = 10 but that isn't larger than 11. We can rule this out.

Choice D is a triangle since

any two sides sum to a value larger than the third side

Choice E is a triangle. We have an equilateral triangle with all sides the same length, and all angles the same value (60 degrees). This is another answer.

Choice F is similar to choice C. We have the first two sides add to something smaller than the third side (4+8 = 12 is smaller than 13). We can rule this out.

english maybe i can ..