Area of a Rectangle* 

A=LW
Area = (Length)(Width)
*The alternative version A=bh is more commonly used: Area=(base)(height). 
Imagine designing a book cover that will have margins on all sides around an area with text and graphics also called the print area of the cover. The book cover will have white space in the margins which are 1 inch wide and 1.5 inches high. The area with print inside of the margins will have a total area of 48 inches. What will be the length and width of the whole book cover to optimize the 48 inches of print area in the center of the book cover with the specified margins?
To complete this problem you will need to know the formula for the area of a rectangle which is area equals length times width.
Knowing that the margins are 1 inch wide and 1.5 inches high, you can write an equation for the area of the book cover using a quantity to represent the length and width of the book cover. Because 1.5+1.5=3 the length of the book cover will be represented by the quantity: (x+3); and because 1+1=2, the width of the book cover will be represented by the quantity: (y+2).







1 
w 
1 

1.5 



1.5 
h 

y 



x 
Print 
x 

y 
1.5 



1.5 

1 

1 


Length (or h for "height") = (x+3)
& Width = (y+2);
therefore...
A= (x+3)(y+2) is the primary equation in solving this problem. The secondary equation is formed by knowing that the book cover has 48 inches of printing area. Therefore, the secondary equation is 48=xy.
Later in this problem the derivative of the equation for the area of the book cover will be needed. The Simple Power rule and the Constant rule are used to find the derivative of the area in steps below.
Domain of X Matters Because X is Solved For First and Y Depends on X
From looking at the secondary equation "xy=48", it is clear that x cannot be 0 or less than 0 because the length must be positive, since we don't count in negative inches, and the length multiplied by the width must equal the positive natural number of 48.
