Make as many triangles with the side measurements of 6, 8, and 10 cm.
To determine how many possible triangles can be formed with side measurements of 6, 8, and 10 cm, we need to apply the triangle inequality theorem. According to this theorem, 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, the three sides given are 6 cm, 8 cm, and 10 cm. Let's check if the triangle inequality is satisfied with each combination of sides:
1. 6 cm + 8 cm > 10 cm - This is true since 6 + 8 = 14, which is greater than 10.
2. 6 cm + 10 cm > 8 cm - This is true since 6 + 10 = 16, which is greater than 8.
3. 8 cm + 10 cm > 6 cm - This is true since 8 + 10 = 18, which is greater than 6.
Since all three combinations satisfy the triangle inequality, we can conclude that it is possible to form a triangle with side measurements of 6 cm, 8 cm, and 10 cm.
To determine how many distinct triangles can be formed, we need to consider the different possible combinations of the three sides. Since the three sides are fixed, the only variation comes from the order in which they are used to form a triangle.
Using the given sides (6 cm, 8 cm, and 10 cm), we can create three distinct triangles by selecting different combinations of sides:
1. Triangle 1: 6 cm, 8 cm, 10 cm
2. Triangle 2: 6 cm, 10 cm, 8 cm
3. Triangle 3: 8 cm, 10 cm, 6 cm
Therefore, there are three distinct triangles that can be formed using side measurements of 6 cm, 8 cm, and 10 cm.