Question

if fj = w and hj = 2w - 40, find fj in parallelogram fghi.

Explanation:

Step1: Recall parallelogram diagonals property

In a parallelogram, the diagonals bisect each other. So, \( FJ = HJ \).

Step2: Set up the equation

Given \( FJ = w \) and \( HJ = 2w - 40 \), since \( FJ = HJ \), we have the equation:
\( w = 2w - 40 \)

Step3: Solve for \( w \)

Subtract \( w \) from both sides:
\( 0 = w - 40 \)
Add 40 to both sides:
\( w = 40 \)
Since \( FJ = w \), then \( FJ = 40 \).

Answer:

\( 40 \)