A box with no top is to be constructed from a piece of cardboard whose Width measures x inch
and whose length measures 3 inch more than the width
the box is to be formed by cutting squares that measure 1 inch on each side of the 4 corners and then folding up the sides
If the volume of the box is 180 inch then what are the dimensions
Now I am trying to solve it through
Volume=L * W * Height
Length = 3+x
Width = x
Height 1inc
and Volume 180 inch
An answer-er came up with this solution>
If you make a sketch you will see that the
length = 3+x - 2 = x+1
and the width is
x-2
the height will be 1
Volume = (x+1)(x-2)(1) = 180
x^2 - x - 2 - 180 = 0
x^2 - x - 182 = 0
(x-14)(x+13) = 0
x = 14 or x = -13, but clearly x > 0
box is x+1 by x-2 by 1
or
15 by 12 by 1
check: what is 15*12*1 ?
is the length of 15 greater than the width of 12 by 3 ?
BUT
It is wrong the multiple choices for this question are >>>
1. 17 inch by 14 inch
2. 21 inch by 18 inch
3. 20 inch by 17 inch
Hi HM
I think I can see where the problem arises.
I found 15 and 12 to be the dimensions of the box.
Which means that the size of the original piece of carboard was 17 by 14, (remember 1 inch is removed on both ends)
Their question was ...
"If the volume of the box is 180 inch then what are the dimensions"
Grammatically, the "dimensions" must refer to the box.
So try 17 by 14 , the size of the cardboard.
Ignoring the fact that their question is poorly worded, it all makes sense.
Orinial cardboard:
width = x
length = x+3 ---- that was given
box:
length = (x+3) - 2 = x+1
width = x-2
height = 1
vol = 1(x-2)(x+1)
= x^2 - x - 2
so x^2 - x - 2 = 180
x^2 - x - 182 = 0
(x-14)(x+13) = 0
x = 14 , and we ignore the other negative answer.
So original cardboard is x by x+3 or 14 by 17
dimensions of box : x-2 by x+1 or 12 by 15
So it depends what we are answering.
How did you ever come up with the equation 3x^2 + 3x - 180 = 0 ????
Reiny !
It is asking for the dimensions of the piece of cardboard !
You are absolutely right, we first find the box's dimensions and then we ADD 2 to each side to get the dimension of the cardboard !
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