Given:
HGFE is a rectangle.
EM = 5x+1
HM = 4x+9
Diagonals intersect at M.
The objective is to find the value of x.
Since the given figure is a rectangle, the diagonals will bisect each other.
So, EM = HM.
[tex]\begin{gathered} 5x+1=4x+9 \\ 5x-4x=9-1 \\ x=8 \end{gathered}[/tex]
Hence, the value of x is 8.
