SOLUTION: Describe the possible lengths of the third side of the triangle given the lengths of the other two sides 4 inches, 7 inches

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Question 258829: Describe the possible lengths of the third side of the triangle given the lengths of the other two sides 4 inches, 7 inches
Found 2 solutions by Fombitz, CharlesG2:
Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website!
Imagine the two lengths like hands on a clock.
Since they're a triangle they cannot exactly line up to form a triangle.
If they were almost on top of each other, like the clock at 12:01, the final leg would be of length,

Now imagine they are 180 degrees apart like at 6:00.
At that point, the final leg would have to be

Since they cannot be either of those two values, the value can be any number in between them.

Answer by CharlesG2(834) (Show Source):
You can put this solution on YOUR website!
Describe the possible lengths of the third side of the triangle given the lengths of the other two sides 4 inches, 7 inches
3 sides: x=4, y=7, z=?
|y-x| < z < x+y (the || is absolute value)
okay since x and y are connected-->
if z=x+y the angle between x and y would be 180 and since there are 180 degrees in a triangle that could not be possible AND -->
if |y-x|=z then the angle between x and y would be 0 and that could not be a triangle either
3 < z < 11