How many different triangles can you make with a perimeter of 12 units
And also use integer values for the length of the sides to investigate how to make up your triangles
What does sure there and sure two mean?
If only integer sides
1 , 10 , 1 nope sum of two must be > third
5 , 4 , 3 sure one
4 , 4 , 4 sure two
3, 3, 6 , nope, straight line
2 , 5 , 5 sure three
2 , 4 , 6 nope
you found a fourth ?
What does sure three and sure two mean?
To find the number of different triangles that can be made with a perimeter of 12 units using integer values for the lengths of the sides, we can use a systematic approach.
We need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
Let's start by listing all possible integer values for the lengths of the sides that satisfy this condition:
1. (1, 1, 10)
2. (1, 2, 9)
3. (1, 3, 8)
4. (1, 4, 7)
5. (1, 5, 6)
6. (2, 2, 8)
7. (2, 3, 7)
8. (2, 4, 6)
9. (3, 3, 6)
10. (3, 4, 5)
Now, let's check if these combinations actually form valid triangles by applying the triangle inequality theorem to each combination:
1. (1, 1, 10): Not a triangle since 1 + 1 = 2 < 10.
2. (1, 2, 9): Not a triangle since 1 + 2 = 3 < 9.
3. (1, 3, 8): Not a triangle since 1 + 3 = 4 < 8.
4. (1, 4, 7): Not a triangle since 1 + 4 = 5 < 7.
5. (1, 5, 6): It is a triangle since 1 + 5 = 6 > 6.
6. (2, 2, 8): Not a triangle since 2 + 2 = 4 < 8.
7. (2, 3, 7): It is a triangle since 2 + 3 = 5 > 7.
8. (2, 4, 6): It is a triangle since 2 + 4 = 6 > 6.
9. (3, 3, 6): It is a triangle since 3 + 3 = 6 > 6.
10. (3, 4, 5): It is a triangle since 3 + 4 = 7 > 5.
Out of the 10 combinations, only 4 of them form valid triangles. Therefore, there are 4 different triangles that can be made with a perimeter of 12 units using integer values for the lengths of the sides.