Determine the range of possible side lengths of the third side AB of Triangle ABC from greatest to least. _

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Determine the range of possible side lengths of the third side AB of Triangle ABC from greatest to least. _

Mathematics
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use triangle inequality: The two shorter sides of any triangle must be greater than the third side. For example, we cannot make a triangle with sides 2,3, 6, or 4,5, 10.|dw:1444354083258:dw|
* sum of the two shorter sides

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So the missing side is less than the other two sides added together?..
The rule is, "the sum of the shorter sides must be greater than the third side". So greater than or smaller than depends if the unknown side is one of the shorter sides or not. Examine each of the diagrams, understand how it works, and find the two cases.
@mathmate I still don't understand how to do this, it's not making sense on what to do after adding together 8 & 10.
The rule is: "the sum of the shorter sides must be greater than the third side". Examples: 1. Can you make a triangle with 8,10 and 100? Solution: shorts sides are 8 and 10. Apply the rule: is 8+10 greater than 100? The answer is no, 8+10=18 is less than 100, so 8,10,100 do not form a triangle. 2. Can you make a triangle with 8, 10 and 20? short sides are 8, 10. Since 8+10=18 is smaller than 20, the answer is no. 3. Can you make a triangle with 8, 10 and 17? short sides are 8,10. Since 8+10>17, it satisfies the rule, so yes, 8,10 and 17 make a triangle. 4. Can you make a triangle with 8,9,10? short sides are 8,9. 8+9>10 so Yes. 5. Can you make a triangle with 7,8,9? short sides are 7,8. Since 7+8 >9, so Yes. 6. Can you make a triangle with 2,8,10? shorts are 2,8. since 2+8=10 (not greater), so No 2, 8, 10 does NOT make a triangle. and so on. So think along these lines and try many times, and see if you can find the limits. Look also at the diagram above to get a better idea of how it works.

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