Kaity draws a scalene triangle. Two sides measure 5 inches and 3 inches? Can the third side measure 3 inches? Why or why not?
In any triangle the sum of two sides must be greater than the third side
so ....
what do you think?
since the triangle is scalene, there can be only one side of length 3. Otherwise it would be isosceles.
To determine if the third side of Kaity's scalene triangle can measure 3 inches, we can use the triangle inequality theorem.
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, we have two sides with lengths of 5 inches and 3 inches. Let's add these two lengths together: 5 + 3 = 8 inches.
Now, according to the triangle inequality theorem, the third side must be shorter than the sum of the other two sides. In other words, the third side must be less than 8 inches in order for a triangle to be formed.
Since the third side in question has a length of 3 inches, it is indeed less than 8 inches. Therefore, it is possible for the third side to measure 3 inches, and a triangle can be formed using these side lengths.
In summary, the third side of the triangle can measure 3 inches because it satisfies the triangle inequality theorem, which requires the sum of any two sides to be greater than the length of the third side.