Question

ad is a perpendicular bisector of bc. find ac. 9x - 12, 6x + 6, ac = ?

Explanation:

Step1: Use Perpendicular Bisector Theorem

Since \( \overline{AD} \) is the perpendicular bisector of \( \overline{BC} \), by the Perpendicular Bisector Theorem, \( AB = AC \). So we set \( 9x - 12 = 6x + 6 \).

Step2: Solve for \( x \)

Subtract \( 6x \) from both sides: \( 9x - 6x - 12 = 6 \), which simplifies to \( 3x - 12 = 6 \). Then add 12 to both sides: \( 3x = 6 + 12 = 18 \). Divide both sides by 3: \( x = \frac{18}{3} = 6 \).

Step3: Find \( AC \)

Substitute \( x = 6 \) into the expression for \( AC \) (which is \( 6x + 6 \)): \( 6(6) + 6 = 36 + 6 = 42 \).

Answer:

42