Jamie is attempting to rope off a triangular area for his vegetable garden. He has three stakes and a total of 56 feet of rope to work with. He wants to use all the rope, and he wants the distance in feet between each stake to be an integer. If the distance between two of the stakes is 19 feet, what is the GREATEST possible distance between any two of the stakes?

Question

e.mccormick · Answer

So, did you find the triangle this makes?

anonymous · Answer

No

e.mccormick · Answer

Well, start with what you know.|dw:1367620586422:dw|

anonymous · Answer

So where would I go from there?

e.mccormick · Answer

We also know that p=19+?+?, right?

anonymous · Answer

Right.

e.mccormick · Answer

Now, what do you remember about the relationships of the sides?

anonymous · Answer

They're all 19?

e.mccormick · Answer

I meant in general.  If sides are the wrong sizes, you can't make a triangle!

e.mccormick · Answer

AFK for a min, they need me to mive my truck...

anonymous · Answer

I honestly have no idea. Haha I'm bad at this stuff.

e.mccormick · Answer

Well, you have 56-19=37 left.

e.mccormick · Answer

If I went over the max for an integer, that would be 36... but the triangle would break.
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anonymous · Answer

Thanks a bunch

e.mccormick · Answer

So you are looking for how long you can make it but not have it break.

e.mccormick · Answer

Now, 19+9+28 also fails.  Sure, it = 56, but 19+9=28.  That would be a line, not a triangle.  So the triangle that works but has the longest possible side is 19, 10, and 27.

e.mccormick · Answer

Do you see how that relates to the sides not breaking and it being a triangle?

anonymous · Answer

Yes I do

e.mccormick · Answer

Not a very deep garden, but really wide!
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