Guidance please, for: Find the width of the margins if the printed area is to be 277.

sagec

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A 22-by-29-inch sheet of paper is to be used for a poster, with the shorter side at the bottom. The margins at the sides and top are to have the same width, and the bottom margin is to be twice as wide as the other margins. Find the width of the margins if the printed area is to be 277.5 in^2.

so far I think the length of the printed area is (29-3x) and the width is (22-2x), but I'm not sure how to solve for the width of the margins because when I tried solving for x with the quadratic equation, I got two answers that didn't make sense in the context of the problem.

If anyone could help, I would appreciate it a lot!
 
A 22-by-29-inch sheet of paper is to be used for a poster, with the shorter side at the bottom. The margins at the sides and top are to have the same width, and the bottom margin is to be twice as wide as the other margins. Find the width of the margins if the printed area is to be 277.5 in^2.

so far I think the length of the printed area is (29-3x) and the width is (22-2x), but I'm not sure how to solve for the width of the margins because when I tried solving for x with the quadratic equation, I got two answers that didn't make sense in the context of the problem.
It would have been very helpful to have been able to see your attempt(s). It's hard to figure out where the difficulty is, when we don't know what has been done.

You haven't defined y our variable or expressions, but I think you are using "x" to stand for the width of the margins, (29 - 3x) is the height of the inner printed part, and (22 - 2x) is the inner width. So you've subtracted "x" from all sides, plus another "x" along the bottom margin.

Code:
paper:

+-------------------+
|  |      x      |  |
|--+-------------+--|
|  | 2           |  |
|  | 9           |  |
|  | -           |  |
| x| 3           |x |
|  | x           |  |
|  |             |  |
|  |             |  |
|  |  22 - 2x    |  |
|--+-------------+--|
|  |     2x      |  |
|  |             |  |
+-------------------+

The area A of a rectangle with width w and height h is given by A = hw. So form the multiplication:

. . . . .(29 - 3x)(22 - 2x)

Set this equal to the given printed area, and solve the resulting quadratic equation by applying the Quadratic Formula.

You will get two fractional values between 1 and 20. The values may not seem "reasonable" (and one of them certainly isn't, in context), but compare the total size of the paper with how relatively little of the paper will be used for printing. The margins then must be large. ;)
 
… printed area is to be 277 …

printed area is to be 277.5 …
Are you using the correct area? Using 277 leads to Irrational solutions (containing √1678), while 277.5 yields Rational solutions. Here's the quadratic equation:

6x^2 - 124x + 410.5 = 0
 
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