What is the smallest perimeter possible for a rectangle whose area is 16in^2 and what are its dimensions? ... ?

Area of the rectangle is given as = 16 square inches

We know

Length * width = Area

Then

Width = Area/Length

Now

Perimeter = 2 (Length + Width)

Perimeter = 2[ {Length + (Area/Length) }]

Perimeter = 2[Length + (16/Length) ]

When d (Perimeter) / d (length) = 0,

Then

2[Length + (16/Length) ] = 0

Length + (16/Length) = 0

Length^2 + 16 = 0

(Length) ^2 = - (4) ^2

Then

Length = 4 inches

Now

Width = Area/Length

= 16/4

= 4 inches.