SOLUTION: A poster is 25 centimeters taller than it is wide. It is mounted on a piece of cardboard so that there is a 5 centimeter border on all sides. If the area of the border alone is 135

Click here to see ALL problems on Polynomials-and-rational-expressions

Question 356487: A poster is 25 centimeters taller than it is wide. It is mounted on a piece of cardboard so that there is a 5 centimeter border on all sides. If the area of the border alone is 1350 centimeters squared, what are the dimensions of the poster?
here is what i have so far, but now i'm stuck:
(w squared + 25w + 10) (w+10) = 1350 + (w squared + 25w) ... then i used FOIL to get:
w cubed + 10w + 10w + 100 = 1350 + (w squared + 25w)
w cubed + 20w = 1250 + (w squared + 25w)
w cubed = 1250 + (w squared + 5w)
thank you for your help!
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A poster is 25 centimeters taller than it is wide.
It is mounted on a piece of cardboard so that there is a 5 centimeter border on all sides.
If the area of the border alone is 1350 centimeters squared, what are the dimensions of the poster?
:
We can do it this way, it's easier, we can get rid of those exponents.
Let x = the poster width
then
(x+25) = poster height
and poster area:
x(x+25) = x^2+ 25x
:
Cardboard dimension (5 cm border adds 10 cm to each dimension)
(x+10) = cardboard width
then
x + 25 + 10 = (x+35) = cardboard height
and cardboard area
(x+10)*(x+35) = x^2 + 45x + 350
:
we know cardboard area - poster area = 1350 sq/cm
therefore:
(x^2 + 45x + 350) - (x^2 + 25x) = 1350
removed brackets
x^2 + 45x + 350 - x^2 - 25x = 1350
Combine
x^2 - x^2 + 45x - 25x = 1350 - 350
20x = 1000
x =
x = 50 cm is the poster width,
then
50 + 25 = 75 cm is the poster height
:
:
See if that works out (Cardboard will be 85 by 60)
(85*60) - (75*50) =
5100 - 3750 = 1350; confirms our solution
:
:
did this make sense to you?