Determine the possible lengths for the third side of a triangle whose first two sides measure a and b.

Question

esshotwired · Answer

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noelgreco · Answer

Can you make a triangle out of three sticks whose lengths are 10, 5, and 4?

anonymous · Answer

you can get the answer in terms of a and b by using the pythagorean theorem.

a^2 + b^2 = c^2

$$c = \sqrt{a^2 + b^2}$$

esshotwired · Answer

But isn't the Pythagorean theorem for right triangles?

anonymous · Answer

yes, that isn't a right triangle?

esshotwired · Answer

i dont think so. it doesnt look like it, but if it isnt, is there another way?

anonymous · Answer

not unless you know an angle.

anonymous · Answer

It looks like a right triangle to me though.

noelgreco · Answer

It simply has to do with the lenths of the sides, and there are a infinite number of those.

Can you answer my previous question?  If you try it, you'll understand the problem better.

esshotwired · Answer

No you cannot with 10, 4, and 5 @NoelGreco

noelgreco · Answer

Aha!  The sum of the lengths of the two shorter sides MUST exceed the length of the longest side.

Now, using >, <, a, and b you should be able to write inequalities.

esshotwired · Answer

so would it be a+x>b?

esshotwired · Answer

@NoelGreco is my answer above correct

noelgreco · Answer

That's it.  I was away for a while.

anonymous · Answer

@esshotwired can you message me?