Answer: Therefore, the answer is:
a) ONE TRIANGLE
b) The sides 4 cm, 6 cm, and 9 cm can form a single triangle.
Explanation:
a) There is exactly ONE TRIANGLE that can be constructed with sides measuring 4 cm, 6 cm, and 9 cm.
b) To determine the number of triangles that can be formed from three given sides, we can use the triangle inequality theorem which states that the sum of any two sides of a triangle must be greater than the third side.
Let's check if the given sides satisfy this inequality:
4 cm + 6 cm > 9 cm (True)
4 cm + 9 cm > 6 cm (True)
6 cm + 9 cm > 4 cm (True)
Since all three inequalities are true, we can conclude that a triangle can be formed using these three sides.
Now, let's determine if there is only one possible triangle that can be formed or if there are more than one. To do this, we can use the fact that the largest side of a triangle must be smaller than the sum of the other two sides. If this is not the case, then it's not possible to form a triangle.
In this case, the largest side is 9 cm. Let's check if it's smaller than the sum of the other two sides:
4 cm + 6 cm = 10 cm (True)
Since 9 cm is smaller than the sum of the other two sides, we can conclude that it's possible to form a triangle, but there is only one possible triangle that can be formed.