two sides of a triangle have lengths 8 and 17. which inqulities represent the possible lenths for the third side, x
To find the possible lengths of the third side, x, of the triangle, we can use the Triangle Inequality Theorem.
The theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
So for a triangle with sides of length 8 and 17, we have:
8 + 17 > x (the sum of the two shorter sides must be greater than the third side)
25 > x
x + 8 > 17 (the sum of the shortest side and the longest side must be greater than the third side)
x > 9
Therefore, the possible lengths for the third side, x, would satisfy the inequalities: 9 < x < 25.