Math Help - Rectangular Packing Box

1. Rectangular Packing Box

A rectangular packing box, similar to a shoebox, without a lid, is 3 times as long as it is wide and half as high as it is long. Each square inch of the bottom of the box costs $0.008 to produce, while each square inch of any side costs$0.003 to produce.

(A) Write an equation that represents the cost, c, of the box as a function of its width x.

(B) Using the function written in part a, determine the dimensions of a box that would cost \$0.69 to produce.

2. Hello,

so its width is x.
We know that its length is 3 times as long as its width, meaning that its length is 3x.
We know that its height is half as long as its length, meaning that its height is (3x)/2.

If you view the box (I recommend you make a sketch), there is one bottom, rectangular, with its sides : length,width,length,width.
So its area is (width * length) = 3x²

For two of the sides, the sides are : length,height,length,height.
So each of their area is (length * height) = 9x²/2

For the last two sides, the sides are : width,height,width,height.
So its area is (width * height) = 3x²/2

And finally, the cost will be ... ?

For question b), solve for x in f(x)=0.69.
This is not hard, just taking square roots
If you struggle with that, let us know.