Question 821503: A box with no top is to be constructed from a piece of cardboard whose length measures 12 inches more than its width. The box is formed by cutting squares that measure 5 inch on each side from the four corners and then folding up the sides.
If the volume of the box 65 in ^3 what are the dimensions of the piece of cardboard?
The Height?
The width?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
v = 65 = Lwh
h = 5
65 = 5Lw
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Lw = 13
L = w + 12
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Lw = 13
(w + 12)w = 13
ww + 12w - 13 = 0
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the above quadratic equation is in standard form, with a=1, b=12, and c=-13
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1 12 -13
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the two real roots (i.e. the two x-intercepts), of the quadratic are:
w = 1
w = -13
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negative width doesn't make sense so use the positive root:
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dimensions of the bottom of the box
w = 1
L = w + 12 = 13
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dimensions of the cardboard:
w= 1 + 10 = 11 inch
L= 13 + 10 = 23 inch
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