How many different triangles can you make with a perimeter of 12 units
do they have integer lengths?
if so
2,5,5
4,4,4
5,4,3
No
To determine the number of different triangles that can be made with a perimeter of 12 units, we first need to consider the triangle inequality theorem. According to this theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
Since the perimeter is 12 units, the sum of the lengths of any two sides of the triangle must be greater than 6 units. Let's consider the possible lengths for the sides of the triangle:
1. If all three sides are 4 units long, we have a triangle with sides of 4 units, 4 units, and 4 units. This is an equilateral triangle.
2. If two sides are 5 units long, and the third side is 2 units long, we have a triangle with sides of 5 units, 5 units, and 2 units. This is an isosceles triangle.
3. If two sides are 4 units long, and the third side is 3 units long, we have a triangle with sides of 4 units, 4 units, and 3 units. This is also an isosceles triangle.
4. If two sides are 4 units long, and the third side is 2 units long, we have a triangle with sides of 4 units, 4 units, and 2 units. This is an isosceles triangle.
5. If one side is 6 units long, and the other two sides are 3 units long, we have a triangle with sides of 6 units, 3 units, and 3 units. This is an isosceles triangle.
6. If one side is 5 units long, and the other two sides are 4 units long, we have a triangle with sides of 5 units, 4 units, and 4 units. This is an isosceles triangle.
So, in total, we can make 6 different triangles with a perimeter of 12 units.