Posted by Brad Paul on September 29, 2002 at 12:28:48:
In Reply to: Re: Precalculus Question posted by Mary on September 28, 2002 at 22:01:47:
: : : Hi,
: : : I'm can't figure out how to approach this question"
: : : Suppose we want to make a poster containing 50 square inches of printed matter surrounded by a 3" border at the top and bottom, and a 2" border along each side. How does the total area of the poster depend on the width of the printed matter?.
: : : Any clues, anyone? Please?
: : Let A be the area of the printed matter, and w the width of the
: : printed matter. If the printed matter is in the shape of a rectangle
: : we can find the height of the printed matter via h=A/w. Let b be the
: : 3 inch border at the top and bottom and c be the 2 inch width of the
: : border along each side. Now with these variable lets write an equation
: : for the total area of the poster. Lets call it Atotal
: : Atotal=(2 c+w)(2 b+A/w)
: : Notice this equation is just a height time width equation. The width
: : is 2 time the border width because there is one on each side and the
: : the width of the printed matter. The height is 2 times the borders
: : plus height written in terms of the Area and width of the printed
: : matter.
: It wouldn't be:
: A = (6+w)(4+w) and therefore A = 24 + w(10+w) since we know the printed matter is a square and the complete poster is a rectangle? Also, how would i show this as a function of w? Would it be expressed as A(w) = 24 + w(10+w) since i need to show how the total area is dependent on the width of the printed material.....Thanks!
I did not take from the question that the printed area is a
square. The question says:
"a poster containing 50 square inches of printed matter"
The words "square inches" is a measure of area not a statement of
geometry. One can say that a circle has the area of 100 square
inches. This is why I express the height of the printed area as
h=A/w. Where A=50 inch2.
Be sure to clearly distinguish between the area of the printed area (my
A) and the total area of the poster (my Atotal)
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