Answer
28 units
Work Step by Step
Using pythagoras theorem in right triangle OCF
$OC^{2}$ =$OF^{2}$ + $FC^{2}$
$5^{2}$ = $4^{2}$ + $FC^{2}$
$FC^{2}$ = $5^{2}$- $4^{2}$
$FC^{2}$ = 25 -16
$FC^{2}$ = 9
FC = 3
In rectangle ABCD
CF = FD, BE = EC because it is given that OE is perpendicular to BC and OF is perpendicular to CD, So OE and OF bisects BC and CD
CD = CF +FD = 3+3 = 6
BC = BE + EC= 4+4 = 8
In a parallelogram opposite sides are equal
therefore AB = CD= 6, AD = BC = 8
The perimeter of ABCD parallelogram is AB+BC+CD+AD = 6+8+6+8 = 28 units.
