Question

A piece of paper is to display 150, space square inches of text. If there are to be one-inch margins on the sides and the top and a two-inch margin at the bottom, what are the dimensions of the smallest piece of paper that can be used? Choose 1 answer:

Answer 1

H=18

W=12

Explanation:

The question says 1 inch margins on the sides AND the top. And THEN a 2 inch margin ONLY on the bottom.

First, solve for y,

A = xy

150 = xy

150/x = y

If the center dimensions is A and its it equals x*y, then plus the margins, the outer dimensions would just be x+(size of margins) for width and y+(size of margins) for height.

This gives us

Width: x + 2

Height: y + 3

Putting height into terms of x: (Substitute y) = 3 + 150/x

Now, since the area of a rectangle is b*h, the equation is:

(x + 2)(3 + 150/x)

Simplify:

3x + 150 + 6 + 300/x

= 3x + 156 + 300/x

Next, we find the derivative of this and then solve for x.

= 3 - 300/x^2

Solving for x:

0 = 3 - 300/x^2

3 = 300/x^2

3x^2 = 300

x^2 = 100

x = 10

Now that we have x, we plug this into the different equations for height and base:

Base=(10) + 2 = 12

Height=3 + 150/(10) =3+15 = 18

Hope this helps!