Question

Apply the triangle inequality theorem to determine which three side lengths form a triangle
8,4,12
8,8,20
20,10,30
10,20,15

Answer 1

To apply the triangle inequality theorem, we need to check if the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

For the given side lengths:
1) 8, 4, 12
The sum of the two shorter sides (8 and 4) is 12, which is equal to the longest side (12). Therefore, this does not form a triangle.

2) 8, 8, 20
The sum of the two shorter sides (8 and 8) is 16, which is less than the longest side (20). Therefore, this does not form a triangle.

3) 20, 10, 30
The sum of the two shorter sides (20 and 10) is 30, which is equal to the longest side (30). Therefore, this does not form a triangle.

4) 10, 20, 15
The sum of the two shorter sides (10 and 15) is 25, which is greater than the longest side (20). Therefore, this forms a triangle.

So, the three side lengths that form a triangle are 10, 20, and 15.