SOLUTION: A poster is 25 cm taller than it is wider. It's mounted on a piece of cardboard so that there is a 5 cm border on all sides. If the area of the border alone is 1350cm^2 what are th

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A poster is 25 cm taller than it is wider. It's mounted on a piece of cardboard so that there is a 5 cm border on all sides. If the area of the border alone is 1350cm^2 what are th      Log On


   

Question 97795This question is from textbook Algebra Structure and Method
: A poster is 25 cm taller than it is wider. It's mounted on a piece of cardboard so that there is a 5 cm border on all sides. If the area of the border alone is 1350cm^2 what are the dimensions of the poster? This question is from textbook Algebra Structure and Method

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A poster is 25 cm taller than it is wider. It's mounted on a piece of cardboard so that there is a 5 cm border on all sides. If the area of the border alone is 1350cm^2 what are the dimensions of the poster?
:
Let x = width of the poster
then
(x+25) = length of the poster
:
Area of the poster:
x(x+25) = x^2 + + 25x
:
Dimensions of the card board
Width = x + 2(5) = (x+10
Length = x+25 + 2(5) = (x+35)
:
Area of cardboard:
(x+35)(x+10) = 0
x^2 + 45x + 350
:
Cardboard area - poster area = border area
x^2 + 45x + 350 - (x^2 + 25x) = 1350
x^2 - x^2 + 45x - 25x + 350 = 1350
20x + 350 = 1350
20x = 1350 - 350
20x = 1000
x = 1000/20
x = 50 cm is the width of the poster
:
50 + 25 = 75 cm is the length of the poster
:
:
Check using the areas:
(85*60) - (75*50) =
5100 - 3750 = 1350 (the given border area}