Of all rectangles with area 256
, which one has the minimum perimeter? Let P
and w
be the perimeter and width, respectively, of the rectangle. Write the objective function in terms of P
and w
. Assume that the width is less than the length if the dimensions are unequal.
(a) Find P
(Type an expression.)
(b) Find the interval of interest of the objective function. (Simplify your answer. Type your answer in interval notation.)
(c) Of all rectangles with area 256
, find the one with dimensions has the minimum perimeter. (Simplify your answers. Use a comma to separate answers as needed.)