SOLUTION: A graphic artist is designing a poster that consists of a rectangular print with a uniform border.The print is to be twice as tall as it width , and the border is to be 3 inches wi

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Question 998674: A graphic artist is designing a poster that consists of a rectangular print with a uniform border.The print is to be twice as tall as it width , and the border is to be 3 inches wide. If the area of the poster is to be 680 in^2,find the dimensions of the print.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
The entire poster is the print plus the border. First assign variables to everything.

system%28h=heightPrint%2Cw=widthPrint%2Cu=widthBorder%2CA=areaPoster%29

These are the known values:
system%28u=3%2CA=680%29.
Description gives h=2w.

The entire poster includes the border and is the area A.
hihlight_green%28%28h%2B2u%29%28w%2B2u%29=A%29

hw%2B2uw%2B2hw%2B4u%5E2-A=0
2w%2Aw%2B2uw%2B2%2A2w%2Aw%2B4u%5E2-A=0
6w%5E2%2B2uw%2B4u%5E2-A=0------quadratic equation in unknown, w. Remember, w is the width of the PRINT.

Keep going like this in all symbols if you want, but now is a good place to substitute the known values and simplify.
6w%5E2%2B2%2A3%2Aw%2B4%2A9-680=0
6w%5E2%2B6w-644=0
highlight_green%283w%5E2%2B3w-322=0%29
Discriminant, 9%2B4%2A3%2A322=9%2B12%2A322=3873
3873=3%2A1291, being two PRIME factors, so just stay with 3873 as discriminant.

highlight%28w=%28-3%2Bsqrt%283873%29%29%2F%282%2A3%29%29, the width of the PRINT (not the poster). You can compute this and then finish finding the height, h.

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
A graphic artist is designing a poster that consists of a rectangular print with a uniform border.The print is to be twice as tall as it width , and the border is to be 3 inches wide. If the area of the poster is to be 680 in^2,find the dimensions of the print.
Width of print: highlight_green%2814%29 inches

Height of print: 2(14), or highlight_green%2828%29 inches