Question

if dg = t and fg = 4t - 48, find dg in parallelogram cdef.
dg = \boxed{}

Explanation:

Step1: Recall parallelogram diagonal property

In a parallelogram, the diagonals bisect each other. So, \( DG = FG \).

Step2: Set up the equation

Given \( DG = t \) and \( FG = 4t - 48 \), we set \( t = 4t - 48 \).

Step3: Solve for \( t \)

Subtract \( t \) from both sides: \( 0 = 3t - 48 \).
Add 48 to both sides: \( 3t = 48 \).
Divide by 3: \( t = \frac{48}{3} = 16 \).

Answer:

\( 16 \)