The lengths of the sides of a triangle are 17, 8, and n. Which of the following must be true?
A. 9 < n < 25
B. n > or equal to 25
C. n < 9
D. 9 < or equal to n < or equal to 25
At first I thought it was B, then I thought it was A or D... is it A? Please help? Thanks
a-b < c < a+b
Looks like A to me.
D is wrong, because if c=9 or 25, the triangle is just a flat line. Try drawing it.
So it is A
What’s the answer then ?
@What's poppin yur wrong
Ah, the classic triangle question! Let's see if I can help you out with some clownish humor.
We know that in a triangle, the sum of any two sides must always be greater than the third side. So let's apply this rule!
If we add the lengths of the two shorter sides, 8 and n, it must be greater than the longest side, which is 17. So we have the inequality 8 + n > 17.
By subtracting 8 from both sides, we can simplify it to n > 9.
Therefore, the length of the third side, n, must be greater than 9.
Now, let's take a look at the options. A says 9 < n < 25. Well, the upper limit 25 may not necessarily hold true because there's not enough information to determine that. So option A is out.
What about option B, n ≥ 25? Well, if n is greater than or equal to 25, it would make the third side longer than the sum of the other two sides, violating the triangle inequality rule. So option B is also out.
Option C, n < 9, is not a valid answer either because we've determined that n must be greater than 9.
That brings us to option D, 9 ≤ n ≤ 25. Since n must be greater than 9 but we can't determine if it's greater than 25, option D is the most accurate choice.
So, my dear friend, the correct answer is D. I hope I cleared up your confusion with a touch of clownish humor!
To determine which of the given options is true, we need to use the triangle inequality theorem. According to this theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's apply this theorem to the given triangle with side lengths 17, 8, and n:
1. The sum of the lengths of the two known sides (17 and 8) must be greater than the length of the third side (n):
17 + 8 > n
25 > n
From this inequality, we can conclude that n must be less than 25. So, the option D (9 ≤ n ≤ 25) is correct.
However, we still have to check the other condition: n > 9.
2. The length of the third side (n) must also be greater than the difference between the lengths of the other two sides (17 - 8 = 9):
n > 9
Now, let's evaluate option A (9 < n < 25) using the information we have:
9 < n
25 > n
Since both conditions n > 9 and n < 25 hold true, we can conclude that option A is also correct.
Therefore, the correct answer is A (9 < n < 25).
C
C
C
C
C
B
B
A