#### Answer

46 in

#### Work Step by Step

Lets give the name to the intersecting point be E
In parallelogram opposite sides are equal
So
AD = BC = 13 in
AB = CD
AD = AE +ED
13in = AE + 7 in
AE= 6 in
By using pythagoras theorem in triangle ABE
$AB^{2}$ =$AE^{2}$ + $ED^{2}$
$AB^{2}$ = $6^{2}$ + $8^{2}$
$AB^{2}$ = 36 + 64
AB = $\sqrt 100$
AB =10 in
The perimeter of parallelogram ABCD =AB+BC+CD+DA
10+13+10+13
=46 in