If x is the page width,
we know the height is 60/x
a = (x-1)(60/x - 2)
we know the height is 60/x
a = (x-1)(60/x - 2)
To find a function for the area of the printed region, let's break it down. The width of the printed region would be x - (1/2 + 1/2) inches, since we subtract the margins on both sides. Similarly, the height of the printed region would be x - (1 + 1) inches, accounting for the top and bottom margins.
Now, to find the area of the printed region, we can simply multiply the width and height. So, our function in terms of x would be:
A(x) = (x - 1) * (x - 2)
Voila! That should do the trick. Just plug in the value of x, and you'll find the area of the printed region according to the strict specifications of this book designer.
Let's assume the width of the printed region is x inches.
The total width of the page, including the margins on both sides, is (x + 2 * (1/2)) = (x + 1) inches.
The height of the printed region is the total height of the page minus the margins at the top and bottom, which is (1 - 2 * (1/2)) = 0 inches.
However, since the book designer specified that each page should have an area of 60 square inches, we can't have a height of 0 inches. Therefore, we need to consider the total height of the page in our calculations.
The total height of the page, including the margins at the top and bottom, is (x + 2 * 1) = (x + 2) inches.
The area of the printed region is then given by the product of the width and height:
Area = (x + 1) * (x + 2).
Thus, the function giving the area of the printed region in terms of x is:
A(x) = (x + 1) * (x + 2).
Let's assume that the width of the printed region is "w" and the height is "h." Since the book designer specified 1-in margins at the top and bottom, and 1/2-in margins on the sides, we can determine the dimensions of the printed region as follows:
Width of the printed region: w = x - 2(1/2) (subtracting the margins on both sides)
Height of the printed region: h = x - 2(1) (subtracting the margins at the top and bottom)
Now, we know that the area of a rectangle is given by multiplying its length and width. Therefore, the area of the printed region can be found by multiplying the width and height:
Area of the printed region: A = w * h
= (x - 2(1/2)) * (x - 2(1))
= (x - 1) * (x - 2)
So, the function in the variable x giving the area of the printed region is:
A(x) = (x - 1)(x - 2)