The printed matter on a 12 by 24 centimeter page of a book must cover 64 square centimeters. If all margins are to be the same width, how wide should the margins be?

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- Jun 25th 2008, 11:25 AMcechmanek32Find the width of a frame
The printed matter on a 12 by 24 centimeter page of a book must cover 64 square centimeters. If all margins are to be the same width, how wide should the margins be?

- Jun 25th 2008, 11:38 AMTheEmptySet
So we need a few formulas to start.

The area of a rectangle is

We know the area

We also know that the length is five more than the width so

and that the width is W.

Now we evaluate the area formula to get

So now using the zero product priciple we set each factor equal to zero to get

and

Since we are talking about the width of a frame the negative solution doesn't make sense so we are left with the width of the frame is 7 in.

Good luck. - Jun 25th 2008, 11:46 AMTheEmptySet
Let x be the size of the margins. Then the length of the printed matter is and the width is

Using the Area formula from the above post we get

we can factor a 2 out of each factor on the left hand side to get

now we can reduce the equation by dividing both sides by 4 to get

Now we expand the right hand side to get

So we get that x=14 or x=4

We reject the first solution becuase if we plug it back into the original equation the length and width are negative so x =4 is the solution.

The margins should be 4cm - Jun 25th 2008, 11:49 AMMoo
Hello,

Attachment 6970

Edit : uuum, too late :( - Jun 25th 2008, 01:39 PMmasters
But, you added another element....a diagram. Diagrams are cool. Like driving in a red convertible.http://www.clicksmilies.com/auswahl/auto003.gif