Question

what is the value of p?
image of a geometric figure with segments labeled 96, p+60, 96, 3p and a right angle at f

Explanation:

Step1: Use the Angle Bisector Theorem

Since \(HI = HG = 96\), by the Angle Bisector Theorem (in a triangle, if a ray bisects an angle of the triangle, then it divides the opposite side into segments proportional to the adjacent sides. Here, for \(\triangle GIL\) (assuming \(IL\) is the side), and the angle - bisector \(IF\)), we have \(3p=p + 60\).

Step2: Solve the equation for \(p\)

Subtract \(p\) from both sides of the equation \(3p=p + 60\).
\(3p−p=p + 60−p\)
\(2p=60\)
Divide both sides by 2: \(p=\frac{60}{2}\)

Answer:

\(30\)