A triangle has side lengths of
6 inches
6 inches
Any length less than 12 inches.
How many triangles are possible?
I think only one triangle is possible, one where all sides measure 6 inches
Did you not read Steve's answer to your previous question regarding the condition to have a triangle?
http://www.jiskha.com/display.cgi?id=1463702386
So is it no triangles are possible then?
To determine the number of possible triangles, we can use the triangle inequality theorem. According to this theorem, for a triangle with side lengths a, b, and c, the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, we have a triangle with side lengths of 6 inches, 6 inches, and any length less than 12 inches. Let's consider the possible scenarios:
1) If the length of the third side is less than 6 inches, then it would not satisfy the triangle inequality theorem, as the sum of the two shorter sides (6 inches and less than 6 inches) would not be greater than the length of the longer side (6 inches). Therefore, no triangle is possible in this case.
2) If the length of the third side is equal to 6 inches, then the triangle would be degenerate (a straight line). However, a degenerate triangle is still considered a valid triangle. So, there is one possible triangle in this case.
3) If the length of the third side is greater than 6 inches but less than 12 inches, then it would satisfy the triangle inequality theorem. Thus, there are infinite possibilities within this range.
In conclusion, there is one possible triangle with side lengths of 6 inches, 6 inches, and any length less than 12 inches.