Question

Which side lengths can represent the sides of a triangle?


Answers available in ...
10Take this time to do your
best on this question.
A)
3
, 5, 6
B)
2
, 3, 5
C)
1, 2, 3
D)
2, 5, 8

Answer 1

the key to this question is to know that the sum of ANY two sides of a triangle wil ALWAYS be greater than the reaming side.
This is a theorem.

Can you now solve?

Answer 2

Triangle Inequality Theorem
One side of a triangle is less than the sum of the other two.
For each triple of potential side lengths do the following:

A) 3 , 5, 6
1) Is 3 < 5 + 6 YES
2) Is 5 < 3 + 6 YES
3) Is 6 < 3 + 5 YES
The sides of option A can form a triangle. -->

Suppose we had decided to test option B first

B) 2, 3, 5

1) Is 2 < 3 + 5 YES
2) Is 3 < 2 + 5 YES
3) Is 5 < 2 + 3 NO
Therefore, the side lengths do NOT form a triangle

Test the sides of options C and D for practice.