Question

what is dg? dg =

Explanation:

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

Since \(F\) is a point on the angle bisector of \(\angle D\), and \(DG\perp\) one side, \(DE\perp\) the other side. By the property that the distance from a point on an angle bisector to the two sides of the angle is equal, we have \(DG = DE\).
So, \(3t + 2=4t\).

Step2: Solve the equation for \(t\)

Subtract \(3t\) from both sides of the equation \(3t + 2=4t\).
\(3t-3t + 2=4t-3t\), which gives \(t = 2\).

Step3: Find the length of \(DG\)

Substitute \(t = 2\) into the expression for \(DG\) (\(DG=3t + 2\)).
\(DG=3\times2+2\).
First, calculate \(3\times2 = 6\), then \(6 + 2=8\).

Answer:

\(8\)