Question

Two sides of a triangle are 10 mm and 7 mm. Determine the length of the third side from the choices given.(1 point)

Responses

1 mm
1 mm

20 mm
20 mm

5 mm
5 mm

2 mm

Answer 1

[AI-generated answer — Bot GPT 3.5]

The third side of the triangle can be determined using 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 two given sides are 10 mm and 7 mm. Therefore, the sum of these two sides is 10 mm + 7 mm = 17 mm. The length of the third side must be less than 17 mm.

Among the choices given, the only option less than 17 mm is 5 mm. Therefore, the length of the third side is 5 mm.

So, the correct answer is:
5 mm

Answer 2

are you sure i got a different answer

Answer 3

[AI-generated answer — Bot GPT 3.5]

Let's re-evaluate the problem:

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given the two sides are 10 mm and 7 mm, the sum is 17 mm.

To find the possible range of values for the third side:
- The length of the third side must be greater than the positive difference between the two given sides: 10 mm - 7 mm = 3 mm
- The length of the third side must be less than the sum of the two given sides: 17 mm

So, the third side must be between 3 mm and 17 mm.

Among the choices given, the only option that falls within this range is 5 mm.

Therefore, the length of the third side is indeed 5 mm.
So, the correct answer is:
5 mm

If you have a different answer, please provide your rationale so we can further discuss it.

Answer 4

i got 1

Answer 5

[AI-generated answer — Bot GPT 3.5]

Let's recheck the calculations:

Given sides: 10 mm and 7 mm
Sum of the given sides: 10 mm + 7 mm = 17 mm

According to the triangle inequality theorem, the length of the third side of the triangle must be greater than the positive difference between the two given sides (|a - b|) and less than the sum of the two given sides (a + b).

In this case:
- Lower limit: |10 mm - 7 mm| = 3 mm
- Upper limit: 10 mm + 7 mm = 17 mm

Between 3 mm and 17 mm, the only option presented in the list is 5 mm.

So, based on the initial information provided, the length of the third side of the triangle is 5 mm.

If you are still getting a different answer, please let me know your reasoning so we can discuss further.