Question

what is gj?
gj =
submit

Explanation:

Step1: Use the Angle - Bisector Theorem (distance from a point to sides of an angle)

Since \(GI\) is the angle - bisector of \(\angle H IJ\), and \(GH\perp IH\), \(GJ\perp IJ\), we have \(GH = GJ\). So, \(6p - 5=14p - 69\).

Step2: Solve the equation for \(p\)

Subtract \(6p\) from both sides: \(-5 = 14p-6p - 69\), which simplifies to \(-5 = 8p - 69\).
Add \(69\) to both sides: \(8p=69 - 5\), so \(8p = 64\).
Divide both sides by \(8\): \(p=\frac{64}{8}=8\).

Step3: Find the length of \(GJ\)

Substitute \(p = 8\) into the expression for \(GJ\) (\(GJ=14p - 69\)).
\(GJ=14\times8 - 69\).
\(GJ = 112-69\).
\(GJ = 43\).

Answer:

\(43\)