Question

A triangle with sides a=8

and c=10
. If side b=3
, would it create a triangle? Enter 1 for “yes” and 2 for “no.”(1 point)
IT'S NOT 2

Answer 1

[AI-generated answer — Bot GPT 3.5]

1

Answer 2

THX

Answer 3

[AI-generated answer — Bot GPT 3.5]

You're welcome! If you have any more questions, feel free to ask.

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)

Responses

22
22

24
24

15
15

30

Answer 5

[AI-generated answer — Bot GPT 3.5]

To determine the length of the third side of the triangle, you can use 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.

In this case, the first two sides measure 10 and 12. Let's check if the sum of these sides is greater than the third side:
10 + 12 = 22

Since the sum of the two given sides (10 and 12) is 22, the third side must be less than 22 for the triangle to be valid.

Therefore, the correct answer from the choices provided is:
15

Hence, the length of the third side of the triangle is 15.

Answer 6

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

10 cm
10 cm

8 cm
8 cm

6 cm
6 cm

5 cm

Answer 7

[AI-generated answer — Bot GPT 3.5]

To determine which of the following choices cannot be the measure of the third side of the triangle, we can use the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that two sides of the triangle measure 4 cm and 9 cm, we can check which of the choices cannot be the measure of the third side:

1. 4 + 9 = 13
2. 9 + x = 10 (For x = 1, the sum is 10)
3. 4 + x = 8 (For x = 4, the sum is 8)
4. 4 + 9 = 13

Therefore, the sum of the lengths of the two given sides is 13 cm, which means the measure of the third side must be less than 13 cm for the triangle to be valid.

From the choices provided:
The measure of the third side cannot be 10 cm or 8 cm because they make the sum greater than 13 cm.

Therefore, the correct answer is:
5 cm

Hence, the measure of the third side of the triangle cannot be 5 cm.

Answer 8

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)

Responses

1
1

11
11

2
2

9

Answer 9

[AI-generated answer — Bot GPT 3.5]

To determine which option could be the third side of a triangle based on the Triangle Inequality Theorem, we need to consider that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that the first two sides measure 4 and 6, let's check the options:

1. 4 + 6 = 10
2. 4 + x = 1 (Not possible because 4 + 1 is less than 6)
3. 6 + x = 2 (Not possible because 6 + 2 is less than 4)
4. 4 + 6 = 10

Therefore, the possible length for the third side must be less than the sum of the given sides, which is 10.

From the options provided, the third side could be:
9

Therefore, the option "9" could be the third side of a triangle based on the Triangle Inequality Theorem.

Answer 10

Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point)

Responses

2, 7, 6
2, 7, 6

9, 4, 3
9, 4, 3

8, 1, 7
8, 1, 7

12, 10, 22

Answer 11

[AI-generated answer — Bot GPT 3.5]

To determine which group of side measures will form a triangle, we can apply 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 check each group of side measures:

1. For the group 2, 7, 6
- 2 + 7 = 9 and 6 > 9 (The sum of the two shorter sides is greater than the third side)
This group can form a triangle.

2. For the group 9, 4, 3
- 9 + 4 = 13 and 3 < 13 (The sum of the two shorter sides is greater than the third side)
This group can form a triangle.

3. For the group 8, 1, 7
- 8 + 1 = 9 and 7 < 9 (The sum of the two shorter sides is greater than the third side)
This group can form a triangle.

4. For the group 12, 10, 22
- 12 + 10 = 22 and 22 = 22 (The sum of the two shorter sides is equal to the third side, this does not form a triangle as per the theorem)
This group cannot form a triangle.

Therefore, the group of side measures that will form a triangle is:
- 2, 7, 6
- 9, 4, 3
- 8, 1, 7

These groups satisfy the Triangle Inequality Theorem and can form a triangle.