#### Answer

4$\sqrt 29$m

#### Work Step by Step

In parallelogram if adjacent sides are equal then it will become rhombus
In rhombus diagonals are perpendicular bisectors
So if assume the point of intersection of both the diagonals as E, so EC = EA = 2m and BE = ED = 5m and $\angle$ CED = 90$^{\circ}$
By pythagoras theorem
$CD^{2}$ =$CE^{2}$ + $ED^{2}$
= $5^{2}$ + $2^{2}$
= 25 + 4 = 29
CD = $\sqrt 29$ m
As we know in rhombus all the sides are equal
therefore AB=BC=CD=DA
therefore perimeter = AB+BC+CD+DA
= $\sqrt 29$+$\sqrt 29$+$\sqrt 29$+$\sqrt 29$
=4$\sqrt 29$m