Question 116489This question is from textbook Algebra: structure and method: book 1
: A rectangular piece of cardboard is 20 cm longer than it is wide. Squares, 10 cm on each side, are cut from the corners of the cardboard, and the sides are folded up to make an open box whose volume is 8L (remember, 1L=1000 cm^3). Find the dimensions of the original piece of cardboard. PLEASE HELP ME!!!!!!
This question is from textbook Algebra: structure and method: book 1
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A rectangular piece of cardboard is 20 cm longer than it is wide.
Squares, 10 cm on each side, are cut from the corners of the cardboard, and the sides are folded up to make an open box whose volume is 8L
(remember, 1L=1000 cm^3).
Find the dimensions of the original piece of cardboard.
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Original Dimensions:
Let the width be "x" cm ; The length is "x+20" cm
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Dimensions after cutting:
width is x-20 cm ; length is x+20-20 = x cm
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Volume after cutting and folding:
EQUATION:
V = l*w*h
8L = 8000 cm^3 = x*(x-20)*10 cm^3
10x(x-20) = 8000
x(x-20) = 800
x^2-20x-800 = 0
x = [20 +- sqrt(400-4*-800)]/2
x = [20 +- sqrt(3600)]/2
x = [20 +- 60]/2
x= 40
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Original width = x = 40 cm
Original length = x+20 = 60 cm
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Cheers,
Stan H.
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