Question

what is the length of \\(\overline{bc}\\)?

enter your answer in the box.

\\(\square\\) units

(image of an isosceles triangle with triangle abc, base bc labeled x, side ac labeled x + 9, side ab labeled 2x - 8, angles at c and b are equal)

Explanation:

Step1: Identify triangle type

The triangle has two equal base angles, so it's isosceles. Thus, \( AC = AB \).
\( AC = x + 9 \), \( AB = 2x - 8 \), so \( x + 9 = 2x - 8 \).

Step2: Solve for \( x \)

Subtract \( x \) from both sides: \( 9 = x - 8 \).
Add 8 to both sides: \( x = 17 \).

Step3: Find \( BC \) length

\( BC = x \), so substitute \( x = 17 \).
\( BC = 17 \) units.

Answer:

17