Question

In rectangle MNPQ with side MN = 16 in, point L is the midpoint of PQ and m∠QLM = 45°. Find the perimeter of the rectangle.

Answer 1

See the attached figure

we know that
MN=16 in-------------> PQ=MN
PQ=16 in
L is the midpoint of PQ-----------> distance QL=PQ/2
QL=8 in
if m∠QLM = 45°
then 
MQ=QL
MQ=8 in

Perimeter=[MN]*2+[MQ]*2=16*2+8*2=48 in

the answer is 48 in