Determine whether it is possible to draw a triangle with sides having the given measures. If possible, write yes. If not possible write no and make a sketch demonstrating why it isn’t possible

No, it is not possible to form a triangle with these side lengths.

The sketch is provided below

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Explanation:

The triangle inequality theorem says that the sum of any two sides must be larger than the third side.

But notice that 5+6 = 11 which is not larger than 12.

I recommend cutting out slips of paper that are 5 inches, 6 inches and 12 inches long. You can also use software to get the job done, which is what I did. You should see that it is impossible to form a triangle. If you place the 5 inch and 6 inch slips on either end of the 12 inch portion, then you should see the we effectively have an open-ended "triangle". I'm putting it in quotes because we don't have a triangle forming, but instead what looks to be an incomplete version of it.

The sketch of what I'm referring to is shown below. I used Geogebra to make the drawing. Imagine the red and blue segments able to swing freely while the green horizontal segment stays completely still. No matter how the red and blue segments rotate, they will never meet up to form a triangle.

The dashed circles show the range of motion that is possible for each swinging red and blue segment. If the red and blue segments lay perfectly on top of the green segment, they add to 5+6 = 11, which comes up short of the 12 inch segment.

5/8 beds for each square yard

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