SOLUTION: A rectangular piece of cardboard is to be formed into an uncovered box. The piece of cardboard is 2 centimeters longer than it is wide. A square that measures 3 centimeters on a si

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Question 341622: A rectangular piece of cardboard is to be formed into an uncovered box. The piece of cardboard is 2 centimeters longer than it is wide. A square that measures 3 centimeters on a side is cut from each corner. When the sides are turned up to form the box, its volume is 765 cubic centimeters. Find the dimensions, in centimeters, of the original piece of cardboard.
PLEASE help.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular piece of cardboard is to be formed into an uncovered box.
The piece of cardboard is 2 centimeters longer than it is wide.
A square that measures 3 centimeters on a side is cut from each corner.
When the sides are turned up to form the box, its volume is 765 cubic centimeters.
Find the dimensions, in centimeters, of the original piece of cardboard.
:
Let x = the width of the original cardboard
then
(x+2) = the length of the original cardboard
:
The dimensions of the box(the squares will subtract 6 cm from the length & width):
(x-6) = the width
(x+2-6) = (x-4) is the length
3 cm is the height
therefore
765%2F3 = 255 is the area of the base of the box
therefore
(x-6)*(x-4) = 255
FOIL
x^2 - 4x - 6x + 24 = 255
:
x^2 - 10x + 24 - 255 = 0
:
x^2 - 10x - 231 = 0
Use the quadratic formula to find x (the width the original cardboard)
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
in this equation: a=1; b=-10; c= -231
x+=+%28-%28-10%29+%2B-+sqrt%28-10%5E2-4%2A1%2A-231+%29%29%2F%282%2A1%29+
:
x+=+%2810+%2B-+sqrt%28100+-+%28-924%29+%29%29%2F2+
x+=+%2810+%2B-+sqrt%28100+%2B+924+%29%29%2F2+
x+=+%2810+%2B-+sqrt%281024+%29%29%2F2+
we only want the positive solution here
x+=+%2810+%2B+32%29%2F2+
x = 42%2F2
x = 21 cm is the width of the cardboard
and
21 + 2 = 23 is the length
:
:
Check this by finding the volume using these dimensions, subtracting 6 cm
15* 17 * 3 = 765; confirms our solution
:
The cardboard is 23 by 21 cm