Question

ad is a perpendicular bisector of bc. find ac. 4x + 6 2x + 12 ac = ?

Explanation:

Step1: Use the Perpendicular Bisector Theorem

Since \( \overline{AD} \) is the perpendicular bisector of \( \overline{BC} \), by the Perpendicular Bisector Theorem, \( AB = AC \). We know \( AB = 4x + 6 \) and \( AC = 2x + 12 \), so we set up the equation:
\( 4x + 6 = 2x + 12 \)

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides:
\( 4x - 2x + 6 = 12 \)
\( 2x + 6 = 12 \)

Subtract 6 from both sides:
\( 2x = 12 - 6 \)
\( 2x = 6 \)

Divide both sides by 2:
\( x = \frac{6}{2} = 3 \)

Step3: Find \( AC \)

Substitute \( x = 3 \) into the expression for \( AC \) (\( 2x + 12 \)):
\( AC = 2(3) + 12 = 6 + 12 = 18 \)

Answer:

18