Question

ad is a perpendicular bisector of bc. find ac. a 10x - 5 4x + 25 ac = ? b d c

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 \( 10x - 5 = 4x + 25 \).

Step2: Solve for \( x \)

Subtract \( 4x \) from both sides: \( 10x - 4x - 5 = 25 \), which simplifies to \( 6x - 5 = 25 \). Then add 5 to both sides: \( 6x = 30 \). Divide both sides by 6: \( x = 5 \).

Step3: Find \( AC \)

Substitute \( x = 5 \) into the expression for \( AC \) (which is \( 4x + 25 \)): \( 4(5) + 25 = 20 + 25 = 45 \).

Answer:

\( 45 \)