## anonymous 5 years ago a page of print is to contain24in^2 of printed region,a margin of 1and1/2 at the bottom,and a margin of 1in.at the sides..what are the dimensions of the smallest page that will fill these requirements?

1. anonymous

A great reference. Thanks godnod. Let me see if I can put it together and held ronadelossantos. Let y equal one dimension of the printed material. Let x = the other dimension of the printed material. It is stated that the printed material is 24 sq. inches. Thus: xy=24. We will use that information later. One dimension of the paper (including the margins) will be x+1 and the other dimension is y+2. Returning to the xy=24 we can say y=24/x. We now have enough information to solve.

$A=(x+1)((x/24)+2)$ This becomes: $24x/x+2x+24/x+2$ $24+2x+24/x+2$ $2x+24/x+26=A$ $2x+24x ^{-1}+26=Area$ Differntiating and set zero for min/max

A' = 0$A'=2-24x ^{-2}=0$

$-24=-2x ^{2}$ $x ^{2}=12$ $x=2\sqrt{3}$ one dimension solve for y y=24/x $y=24/(2\sqrt{3}=12/\sqrt{3}=4\sqrt{3}$