Question

ad is a perpendicular bisector of bc. find ac. 11x - 2 5x + 10 ac = ? b d c

Explanation:

Step1: Use Perpendicular Bisector Theorem

Since \( \overline{AD} \) is the perpendicular bisector of \( \overline{BC} \), \( AB = AC \). So \( 11x - 2 = 5x + 10 \).

Step2: Solve for \( x \)

Subtract \( 5x \) from both sides: \( 11x - 5x - 2 = 10 \) → \( 6x - 2 = 10 \).
Add 2 to both sides: \( 6x = 10 + 2 \) → \( 6x = 12 \).
Divide by 6: \( x = \frac{12}{6} = 2 \).

Step3: Find \( AC \)

Substitute \( x = 2 \) into \( AC = 5x + 10 \):
\( AC = 5(2) + 10 = 10 + 10 = 20 \).

Answer:

\( 20 \)