Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point)

Question

Responses

8, 8, 20

10, 20, 15

20, 10, 30

8, 4, 12

Answer 1

To apply the Triangle Inequality Theorem, we need to check if the sum of any two side lengths is greater than the third side length.

For the first set of side lengths, 8, 8, 20, we have:

8 + 8 = 16 < 20

So, the first set of side lengths does not form a triangle.

For the second set of side lengths, 10, 20, 15, we have:

10 + 15 = 25 > 20
10 + 20 = 30 > 15
20 + 15 = 35 > 10

So, the second set of side lengths forms a triangle.

For the third set of side lengths, 20, 10, 30, we have:

20 + 10 = 30 < 30

So, the third set of side lengths does not form a triangle.

For the fourth set of side lengths, 8, 4, 12, we have:

8 + 4 = 12 > 12
8 + 12 = 20 > 4
4 + 12 = 16 > 8

So, the fourth set of side lengths forms a triangle.

Therefore, the sets of side lengths that form a triangle are:

10, 20, 15

8, 4, 12