Question 71812This question is from textbook Algebra
: a poster is 25 cm taller than it is wide. it is 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 1350 cm^2, what are the dimensions of the poster?
This question is from textbook Algebra
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! a poster is 25 cm taller than it is wide. it is 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 1350 cm^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)
:
:
(x + 2(5)) = width of the cardboard the poster is mounted on
(x+10) = width simplified
:
(x + 25 + 2(5)) = length of cardboard
(x + 35) = length simplified
:
Area of card board = (x+10)*(x+35) = (x^2 + 45x + 350)
:
The equation:
cardboard area - poster area = border area ( given as 1350 sq/cm)
(x^2 + 45x + 350) - (x^2 + 25x) = 1350
:
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:
(85*60) - (75*50)
5100 - 3750 = 1350 sq/cm the given area of the border
:
Could you follow this OK, any questions?
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