POW #21, due Monday 3/30
I have a loop of string on my desk and was playing with it last night as I was trying to figure out what to use for a problem this week. I started thinking about both the geometry we did earlier this year, and the material we are into now. Anyway, here goes.
First, find all of the possible triangles I could make with this 12-inch loop of string where all of the sides of each triangle are integers (which in this case would all be positive whole numbers.)
Second, explain whether each triangle is scalene, isosceles, or equilateral, and also whether it is acute, right, or obtuse.
You’ll need to carefully explain how you know you’ve correctly answered both parts of the question, and to include any calculations you might have done.
Be sure to show and explain all your work. An answer without clear & complete explanation is not correct and will not earn a good score. Look at the grading rubric.
XC: Which of the possible triangles in the problem has the greatest area? Make sure you explain how you reached your conclusion.
This POW is really a blast from the past. It is the same as POW #9.
If you remember that one, you’ll recall that there are only three possible triangles. But now, you have a perfect tool to show whether any of these trinagles are right triangles. Be sure to use the Pythagorean converse in your explanation.
You can also use the Pythagorean theorem to get the extra credit portion. (More on this tomorrow.)