Question

3x + 30
48
5x - 12
6
8.25
12
21

Explanation:

Step1: Use the property of perpendicular bisector

Since the line is a perpendicular bisector of the side of the triangle, the two segments \(3x + 30\) and \(5x-12\) are equal. So we set up the equation \(3x + 30=5x - 12\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(30 = 2x-12\).
Add \(12\) to both sides: \(2x=30 + 12=42\).
Divide both sides by \(2\): \(x=\frac{42}{2}=21\).

Answer:

\(21\)