Each page of a book will contain 30 in squared of print, and each page must have 2 inch margins at top and bottom and 1 inch margin at each side. What is the minimum possible area of such a page.
if the page width = w, the height = 30/w
Allowing for two margins on each dimension,
a(w) = (width + 2*2)(30/w + 2*1)
= (w+4)(30/w+2)
= 30 + 2w + 120/w + 8
= 2w + 120/w + 38
area is min where da/dw = 0
da/dw = 2 - 120/w^2
2w^2 = 120
w^2 = 60
w = 7.75
a(7.75) = 68.98 -- call it 69 in2
To find the minimum possible area for a page, we need to subtract the total space occupied by margins from the total area of the page.
Given:
- Each page contains 30 square inches of print.
- The top and bottom margins are 2 inches each.
- The side margins are 1 inch each.
Let's calculate the area of the page:
Total page width = 2 side margins + print width + 2 side margins
Total page width = 1 inch + print width + 1 inch
Total page width = 2 + print width
Total page height = 2 top/bottom margins + print height + 2 top/bottom margins
Total page height = 2 inches + print height + 2 inches
Total page height = 4 + print height
The area of the page is given by:
Page Area = Total page width * Total page height
Page Area = (2 + print width) * (4 + print height)
To find the minimum possible area, we set the width and height of the print area to their minimum values, which are 0.
Page Area = (2 + 0) * (4 + 0)
Page Area = 2 * 4
Page Area = 8 square inches
Therefore, the minimum possible area of the page is 8 square inches.
To find the minimum possible area of a page in a book, we need to calculate the printable area on each page.
Given:
- Each page has a printable area of 30 square inches.
- The top and bottom margins are 2 inches each.
- The left and right margins are 1 inch each.
To calculate the printable area on each page, we need to subtract the margins from the total area.
The total width of the page, including the margins, is 2 inches (top) + 30 inches (printable area) + 2 inches (bottom) = 34 inches.
Similarly, the total height of the page, including the margins, is 1 inch (left) + 8 inches (printable area) + 1 inch (right) = 10 inches.
To find the minimum possible area, we multiply the width and height of the printable area:
Minimum Possible Area = Width * Height
= (34 inches - 2 inches - 2 inches) * (10 inches - 1 inch - 1 inch)
= 30 inches * 8 inches
= 240 square inches.
Therefore, the minimum possible area of such a page in the book is 240 square inches.