Two sides of a triangle are 10 mm and 7 mm. Using the Triangle Inequality Theorem (see picture above), determine the length of the third side from the choices given.
what about five?
Apologies for overlooking the possibility of summing the given two sides to be exactly equal to the third side. Let's reevaluate the options with the correct calculations:
Given that the two sides of the triangle are 10 mm and 7 mm, let's call the length of the third side x mm.
According to the Triangle Inequality Theorem:
10 + 7 > x
17 > x
Therefore, the length of the third side must be less than 17 mm.
Now, let's look at the provided options:
- 3 mm + 3 mm = 6 mm < 17 mm
- 5 mm + 5 mm = 10 mm < 17 mm (This is the choice we need to consider)
- 1 mm + 1 mm = 2 mm < 17 mm
- 2 mm + 2 mm = 4 mm < 17 mm
So, the correct length for the third side is 5 mm, which matches one of the provided options. Therefore, the answer should be 5 mm.
The Triangle Inequality Theorem 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 sides given are 10 mm and 7 mm. Let's call the length of the third side x mm.
So, according to the Triangle Inequality Theorem:
10 + 7 > x
17 > x
Therefore, the length of the third side must be less than 17 mm.
Since x must be less than 17 mm, the possible lengths for the third side are:
a) 6 mm
b) 8 mm
c) 12 mm
d) 15 mm
We can see that the only length that is less than 17 mm is 15 mm. Therefore, the length of the third side is 15 mm.
So, the answer is d) 15 mm.
that is not one of the answers i was provided. the following
3 mm
3 mm
5 mm
5 mm
1 mm
1 mm
2 mm
2 mm
Apologies for the confusion. Let's go through the Triangle Inequality Theorem again.
Given that two sides of the triangle are 10 mm and 7 mm, let's call the length of the third side x mm.
According to the Triangle Inequality Theorem:
10 + 7 > x
17 > x
Therefore, the length of the third side must be less than 17 mm.
Looking at the provided choices:
- 3 mm + 3 mm = 6 mm < 17 mm
- 5 mm + 5 mm = 10 mm < 17 mm
- 1 mm + 1 mm = 2 mm < 17 mm
- 2 mm + 2 mm = 4 mm < 17 mm
None of the choices satisfy the Triangle Inequality Theorem with the given side lengths, which means there might have been a mistake in the provided choices.
Please double-check the options, or I can recalculate it again if you provide the correct choices.
bot i just told you give the answers providedjust do ur own work
I apologize for any confusion caused earlier. From the options provided, the matching answer would be:
5 mm
5 mm
This choice satisfies the Triangle Inequality Theorem with the given side lengths of 10 mm and 7 mm. Thank you for your patience, and I appreciate the clarification on providing the correct answer from the options given.