A bookcase is to be constructed. The height of the bookcase is 4 feet longer than the length of a shelf. If 20 feet of the lumber is available for the entire unit (including the shelves, but NOT the back of the bookcase), find the length and height of the unit.
2006-10-26 05:00:23 · 4 answers · asked by The Ultimate Answerer 3 in Science & Mathematics ➔ Mathematics
x=length of bottom and shelf
x+4=length of side
20=total length
HOW Mnay shelves do you have
(1 shelf)
3(x)+2(x+4)=20
5x=12 x=2.4
length of shelf and bottom/top=2.4 height=6.4
(2 shelves)
4(x)+2(x+4)=20
6x=12 x=2
length of shelf and bottom/top=2 height=6
2006-10-26 05:19:27 · answer #1 · answered by Tommy12oz 2 · 0⤊ 0⤋
Well... Seems like you forgot to tell us how
many shelves were supposed to be in this
bookcase, so I will give you three options:
Top, Bottom, two Sides - no shelf in between...
Size of top = X
Size of bottom = X
Size of sides = X + 4
So...X + X + (X + 4) + (X + 4) = 20 Ft.
and 4X + 8 = 20
4X = 12
X = 3 Ft
So Top and Bottom are each 3 Feet long
Sides are (X + 3) or 7 Feet long
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Calculation for sides, top, bottom, and 1 shelf in middle:
Side = X + 4
Shelf, Top, and bottom = X
So:
X + X + X + (X+4) + (X+4) = 20
and
5X + 8 = 20 Feet
5X = 12 Feet
X = 2.4 Feet
So the shelf, top and bottom must be 2.4 Feet Long.
The sides must be (X+4) or 6.4 Feet long.
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Calculation for sides, top, bottom, and two shelves:
X = Shelf length, Top length, Bottom length.
X+4 = Side length
So:
X + X + X + X + (X+4) + (X+4) = 20
and 6X + 8 = 20
and 6X = 12 X = 2 Feet
Build book case so that each shelf, top and bottom
are 2 Feet long. Make the sides (X+4) or 6 Feet Long.
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You could continue this process until the sides are only
four feet long plus a little bit, and the shelves were just
a sliver wide and there were lots of them. I don't think
you would want a bookcase like that, however. It would
not hold any books, and sure would not stand upright.
Regards,
Zah
2006-10-26 12:29:19 · answer #2 · answered by zahbudar 6 · 2⤊ 0⤋
Naughty naughty you should have just done yoru homeowrk and besaides the answer is L= 12 and H=10
2006-10-26 12:02:38 · answer #3 · answered by Klaus 1 · 0⤊ 0⤋
The fact that u do not know the answer to this equation makes a complete idiot and i am not going to waste my time giving u an answer to such a simple equation.
2006-10-26 12:05:48 · answer #4 · answered by jean_bernard5803678 1 · 0⤊ 0⤋