I have 4 different examples that contain 3 numbers that I need to know if the 3 numbers in each set will form a triangle.
5,2,8
7,8,14
6,6,12
7,9,15
If the sum of the sides of a triangle must equal 180 than the answer is no to all. Right? But I think this is a trick question. Am I right?
NO..
So none of these form a triangle right? Or are you saying no that it's not a trick question.
You are confusing length of sides with the sum of the angles of a triangle.
It is true that the sum of the 3 angles of any triangle will add up to 180º, but you are given the lengths of sides.
One of the basic properties of triangles that the sum of any 2 of the sides must be greater than the third side to form a triangle.
So the first one cannot be a triangle since 5+2 is not greater than 8
The second one does form a triange since
7+8 > 14
7+14 > 8 and
8+14 >7
the third one cannot form a triangle since 6+6 is not greater than 12, as a matter of fact.
What do you think about the fourth question?
To determine whether the given sets of numbers will form a triangle, we need to check if the sum of any two sides of the triangle is always greater than the third side. This is known as the triangle inequality theorem.
Let's apply the triangle inequality theorem to each set of numbers:
1. 5, 2, 8:
- The sum of 5 and 2 is 7, which is less than 8.
- The sum of 5 and 8 is 13, which is greater than 2.
- The sum of 2 and 8 is 10, which is also greater than 5.
In this case, the sum of any two sides is greater than the third side, so a triangle can be formed.
2. 7, 8, 14:
- The sum of 7 and 8 is 15, which is greater than 14.
- The sum of 7 and 14 is 21, which is also greater than 8.
- The sum of 8 and 14 is 22, which is greater than 7.
Again, the sum of any two sides is greater than the third side, so a triangle can be formed.
3. 6, 6, 12:
- The sum of 6 and 6 is 12, which is equal to the third side 12.
In this case, the sum of the two equal sides is not greater than the third side. Therefore, a triangle cannot be formed.
4. 7, 9, 15:
- The sum of 7 and 9 is 16, which is greater than 15.
- The sum of 7 and 15 is 22, which is greater than 9.
- The sum of 9 and 15 is 24, which is also greater than 7.
Similar to the first two sets, the sum of any two sides is greater than the third side, so a triangle can be formed.
Therefore, out of the four sets, only the first three numbers (5, 2, 8) and (7, 8, 14) can form a triangle. The set (6, 6, 12) cannot form a triangle because the sum of the two equal sides is not greater than the third side.