Question

what is the value of p? (note: the image shows a geometric figure with triangle and right angle at h, side lengths 46, 60, and p + 60. the question is to find p, with p = )

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. Here, point \(J\) is on the perpendicular bisector of \(IK\), so \(IJ = KJ\).

Step2: Set up the equation

We know that \(IJ = 6p\) and \(KJ=p + 60\). Since \(IJ=KJ\), we have the equation \(6p=p + 60\).

Step3: Solve the equation for \(p\)

Subtract \(p\) from both sides: \(6p-p=p + 60-p\), which simplifies to \(5p=60\).
Divide both sides by \(5\): \(p=\frac{60}{5}\).

Answer:

\(12\)