# Thread: Find the width of a frame

1. ## Find 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?

2. Originally Posted by cechmanek32
Somebody please help me...I really have no idea what to do. I'm not even sure where to start! Here is my problem, and if someone could show me the steps I Would REALLY appreciate it! Thanks is advance!

The length of a rectangular frame is 5 cm more than the width. The area inside the frame is 84 square cm. Find the width of the frame.
So we need a few formulas to start.

The area of a rectangle is $\displaystyle A=L \cdot W$

We know the area $\displaystyle A=84 in^2$

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

$\displaystyle L=W+5$ and that the width is W.

Now we evaluate the area formula to get

$\displaystyle 84=(W+5)W \iff 84=W^2+5W \iff 0=W^2+5W-84$
$\displaystyle 0= (W+12)(W-7)$

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

$\displaystyle W+12=0 \iff W=-12$ and $\displaystyle W-7=0 \iff W=7$

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.

3. Originally Posted by cechmanek32
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?
Let x be the size of the margins. Then the length of the printed matter is $\displaystyle 24-2x$ and the width is $\displaystyle 12-2x$

Using the Area formula from the above post we get

$\displaystyle 64=(24-2x)(12-2x)$ we can factor a 2 out of each factor on the left hand side to get

$\displaystyle 64=2\cdot 2\cdot (12-x)(6-x)$ now we can reduce the equation by dividing both sides by 4 to get

$\displaystyle 16=(12-x)(6-x)$ Now we expand the right hand side to get

$\displaystyle 16=72-18x+x^2 \iff x^2-18x+56=0 \iff (x-14)(x-4)=0$

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

4. Hello,

Originally Posted by cechmanek32
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?

Edit : uuum, too late

5. Originally Posted by Moo
Hello,

Edit : uuum, too late
But, you added another element....a diagram. Diagrams are cool. Like driving in a red convertible.