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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|dw:1444407821086:dw|
@MrNood meaning..??

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the 3 sides of a triangle have to join up my first sketch show the two known lines essentially joined end to end the third line has to join the ends of those so what is the longest it can be? the second sketch shows the two known lines joined to almost double back on each other. The third line has to join the other ends. So what is the shortest it can be? (assume the known lines are essentially making a straight line )
The shortest side is 8?
no |dw:1444408475372:dw|
Just think about this practically take a stick 10" long take a stick 8" long put them together end to end in the longest straight line HOW LONG is the longest stick that will touch both ends? now put them together next to each other with one end touching like in my second skech What is the shortest stick that will joint the ends now?
18?
if that makes sense to you then go with it what is the shortest?
Less than 18?
if 18 is the longest then of course the shortesdt is less please don't guess - this is a simple practical question - take a minute to think. Look at my sketches It asks the shortest value for the third side given the other sides are 10 and 8 the shortest side joins the ends as shown below: |dw:1444409387968:dw| how long is the joining line?
How would I find the joining line?..
Think of the 2 sticks How long would the third stick be to join up like I showed above? (assume the other sticks are touching all along....
2?
if that makes sense to you then go with it
Okay.

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