Question

Apply the Triangle Inequality Theorem and determine which option could be the third side of a triangle if the first two sides measure 4 and 6.(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine if a third side can form a triangle with sides measuring 4 and 6, we can use the Triangle Inequality Theorem, which states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides.

So, for a third side to form a triangle with sides measuring 4 and 6, it must satisfy the inequality:

Third side < 4 + 6

Simplifying,

Third side < 10

Therefore, any option whose value is less than 10 could be the third side of a triangle.

Answer 2

Two sides of a triangle measure 4 cm and 9 cm. Determine which of the following choices cannot be the measure of the third side.(1 point) Responses

Answer 3

[AI-generated answer — Bot GPT 3.5]

To determine which choice cannot be the measure of the third side, we can use the Triangle Inequality Theorem, which states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides.

So, for the third side to form a triangle with sides measuring 4 cm and 9 cm, it must satisfy the inequality:

Third side < 4 + 9

Simplifying,

Third side < 13

Therefore, any option whose value is greater than or equal to 13 cannot be the measure of the third side.

Answer 4

Determine the length of the third side of a triangle from the choices provided if the first two sides measure 10 and 12.(1 point)

Answer 5

[AI-generated answer — Bot GPT 3.5]

To determine the length of the third side of a triangle when the first two sides measure 10 and 12, we can use the Triangle Inequality Theorem. According to the theorem, the length of any side of a triangle must be less than the sum of the lengths of the other two sides.

So in this case, the third side must satisfy the inequality:

Third side < 10 + 12

Simplifying,

Third side < 22

Therefore, the length of the third side must be less than 22.