Question

Stacey is constructing an triangle out of straws. She measures two sides: 1 3/4 inches and 2 inches. Let the length of the third side of the triangle be x. Write an inequality to show the longest and shortest possible lengths for the third side.

So far, I have:

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Answer 1

Nope, pythagorean theorem applies to right triangles, but if we're talking about any possible triangle then most of those aren't going to be right triangles.

What I do for these problems is imagine the two sides I do know attached at one end and rotate them around with a stretchy side attached to both of the other ends and see how far I can stretch it or close it up until the triangle is a line, and thus, no longer a triangle.

Answer 2

Draw some pictures, I think that'll really be helpful, and I'll guide you along if you still need help. Once you figure it out, you'll be like, "Ohhhhh" =D

Answer 3

So draw out 3 triangles one obtuse, acute, and right with two of the same sides on either side of each angle and we'll talk about it.

Answer 4

Forget that I'll just draw you out a picture, I'm making this more complicated than it has to be.

Answer 5

So these are all possible triangles you can make right? Now what happens as we try to make x as large as possible? What does the triangle look like when we make x as small as possible?

Remember you can't make it so small or too large that it doesn't attach to the other sides, try drawing it out.

Answer 6

Well you're on the right track, but remember, x is the side that's changing, not the other two sides. The other two sides are straws, and straws don't change length.