Gosh, did you draw a picture ? There is one rectangle inside another.
Do you know that area equals width times height ?
Start with the rectangular block of text. It is x inches wide, and its area is 40 square inches.
Clearly, the height of the block of text must be 40/x inches.
x(40/x) = 40
To get the dimensions of the page, we simply add the two respective border widths to both the text-block width and text-block height.
The page width is 0.75 + x + 1
The page height is 1.5 + 40/x + 1
The area function for the page is the product of the page's two dimensions.
If we call the function A, then we have:
A(x) = (0.75 + x + 1)(1.5 + 40/x + 1)
Simplify each factor above (i.e., the expressions inside the parentheses).
That's an answer for part (a). You can multiply the two simplified factors together, if you like. That's another acceptable answer, for part (a).
To solve part (b), is your class using graphing calculators, to zoom in on the lowest point of the curve, to see the coordinates there (i..e, the text-block width and the page area associated with it)?
Once you have a value for the specific page width, you can divide it into the associated area, and the result will be the page height.
I mean, area = width * height, so we have:
height = area/width
Here's a graph of the area function, over the restricted domain [3, 8] inches, to give rough estimates for the width and area.
If you believe that you're supposed to solve part (b) some other way, what is it?
[attachment=0:332x04bj]pagearea.JPG[/attachment:332x04bj]
