In an isosceles triangle, two sides are equal in length. Let's denote the lengths of the sides as follows based on the given information:
- \( AB = x + 17 \)
- \( BC = 2x - 6 \)
Since triangle ABC is isosceles, we can set the lengths of the two equal sides (in this case, assume \( AB \) is equal to \( AC \) and thus set \( AB \) equal to \( BC \)):
\[ x + 17 = 2x - 6 \]
Now, we can solve for \( x \):
- Rearranging the equation: \[ 17 + 6 = 2x - x \] \[ 23 = x \]
Now substituting \( x \) back into the expression for \( BC \):
\[ BC = 2x - 6 \] \[ BC = 2(23) - 6 \] \[ BC = 46 - 6 = 40 \]
Thus, the length of line segment \( BC \) is \( \boxed{40} \).
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