Which of the following sets of side lengths can be used to draw a triangle? Remember the triangle inequality therom
In order for a triangle to be possible with side lengths a, b, and c, it must satisfy 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 third side.
Let's consider the following sets of side lengths:
1. a = 5, b = 2, c = 8
2. a = 3, b = 3, c = 6
3. a = 7, b = 5, c = 4
4. a = 6, b = 10, c = 4
To determine if a triangle can be formed, we need to check if the sum of any two sides is greater than the third side.
1. a + b = 5 + 2 = 7 < c = 8 : Triangle cannot be formed.
2. a + b = 3 + 3 = 6 > c = 6 : Triangle can be formed.
3. a + b = 7 + 5 = 12 > c = 4 : Triangle can be formed.
4. a + b = 6 + 10 = 16 > c = 4 : Triangle can be formed.
Therefore, the sets of side lengths that can be used to draw a triangle are:
2. a = 3, b = 3, c = 6
3. a = 7, b = 5, c = 4
4. a = 6, b = 10, c = 4