Hello, ^_^Engineer_Adam^_^!
The printed area of a rectangular poster is 704 in².
The printed area plus the area of the margins is 1200 in².
Find the dimension of the poster if each of the margins is 4" wide. Code:
: 4 : - x - : 4 :
- * - - - - - - - - * -
4 | | :
- | * - - - - * | :
: | | | | :
: | | | | :
y | |y | | y+8
: | | | | :
: | | x | | :
- | * - - - - * | :
4 | | :
- * - - - - - - - - * -
: - - - x+8 - - - :
The length of the printed area is x.
The height of the printed area is y.
. . Then: .xy = 704 . → . y = 704/x [1]
The length of the poster is x + 8.
The height of the poster is y + 8.
. . Then: .(x + 8)(y + 8) = 1200 [2]
Substitute [1] into [2]: .(x + 8)(704/x + 8) .= .1200
. . which simplifies to: .8x² - 432x + 5632 .= .0
. . Divide by 8: . x² - 54x + 704 .= .0
. . which factors: .(x - 22)(x - 32) .= .0
. . and has roots: .x .= .22, 32 . → . y .= .32, 22
Hence, the dimensions of the printed area is: 22 x 32 inches.
Therefore, the dimension of the poster is: 30 x 40 inches.