A rectangular page is to contain 196 square inches of print.The margins on each side are 1 inch.Find the dimensions of the page such that the least amount of paper is used.
A)17,17
B)29,29
C)18,18
D)15,15
E)16,16

Question

A rectangular page is to contain 196 square inches of print.The margins on each side are 1 inch.Find the dimensions of the page such that the least amount of paper is used. ​
A)17,17
B)29,29
C)18,18
D)15,15
E)16,16

Quizplus · Accepted Answer

The problem can be solved by setting up an equation for the area of the printed region and the margins, then minimizing the total area of the page. Let x and y be the dimensions of the printed area. Given that each margin is 1 inch, the dimensions of the page are (x + 2) and (y + 2). The area of the printed region is 196 square inches, so xy = 196. To minimize the paper used, we want to minimize the total area of the page, which is (x + 2)(y + 2). Since xy = 196, the dimensions x and y that make x and y as close as possible will minimize the total area, making the page nearly square. The square root of 196 is 14, so the dimensions of the printed area are 14 by 14 inches, making the page dimensions 16 by 16 inches.

A Rectangular Page Is to Contain 196 Square Inches of Print.The