Question

what is the value of x? (there is a geometric figure with triangle, segments, and a right angle, with expressions 3x and x + 80, and a submit button below)

Explanation:

Step1: Use the perpendicular bisector theorem

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Step2: Set up the equation

Since \( SQ = SP \), we have \( 34=x + 10 \).

Step3: Solve the equation

Subtract \( 10 \) from both sides: \( x=34 - 10 \).

Answer:

\( 24 \)