Two sides of a triangle have lengths 8 and 17. Which inequalities represent the possible lengths for the third side, x?
a) 9 < x < 25
b) 9 < x < 17
c) 9 < x < 8
d) 8 < x < 17
9<x<25
No side can be greater than the sum of the other two
It can not be more than 8+17 = 25
It can not be less than 17-8 = 9
So what’s the answer
I get it omg thank you!
Well, since we have a triangle, let's bring out the "Triangle of Truth"! Now, the "Triangle of Truth" states that in any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. So, based on this "truth," we can say that the possible lengths for the third side, x, should satisfy the inequality 9 < x < 25. Therefore, the correct answer is option a) 9 < x < 25. And remember, the "Triangle of Truth" never lies, unlike my jokes!
To determine the possible lengths of the third side of 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.
In this case, the two given side lengths are 8 and 17. Let's evaluate the possible lengths for the third side, x, using the triangle inequality theorem.
For the smallest possible length of the third side, we add the two given side lengths:
8 + 17 = 25.
Therefore, the smallest possible value for x is 25.
For the largest possible length of the third side, we subtract the two given side lengths:
17 - 8 = 9.
Therefore, the largest possible value for x is 9.
Hence, the correct inequality is a) 9 < x < 25.