SOLUTION: APPLIED PROBLEMS ( need equation and solution) A rectangular cardboard is to be made into an open box by cutting a 2cm square piece from each corner and turning up the sides. If t

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Question 905317: APPLIED PROBLEMS ( need equation and solution)
A rectangular cardboard is to be made into an open box by cutting a 2cm square piece from each corner and turning up the sides. If the perimeter of the cardboard is 60cm and the volume of the resulting box is 224 cm^3, what are the dimensions of the cardboard.?
Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Let w and L be the dimensions of the cardboard before cutting and folding.

Cut the 2 cm square corners and fold:

Area of the base, %28w-2%2A2%29%28L-2%2A2%29.

Perimeter of the base supposed to be 2%28w-4%29%2B2%28L-4%29=60
2w-8%2B2L-8=60
2w%2B2L=60%2B16
2w%2B2L=76
w%2BL=38

Volume of the box given as 224, so
highlight_green%28%28w-4%29%28L-4%29%2A2=224%29
%28w-4%29%28L-4%29=112

Now just work with the system
highlight%28system%28%28w-4%29%28L-4%29=112%2Cw%2BL=38%29%29 to solve for w and L.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let length of the card board be x
and the width of the card board be y
length of box = (x-4) ( 2 cut from each side)
width of box = (y-4)
height of box = 2 cm
volume of box = l*b*h
224 = (x-4)(y-4)*2
/2
112 = xy-4x-4y+16
96 = xy-4x-4y
2(x+y) = 60
x+y=30
96=xy-4(x+y)
96=xy-4*30
96=xy-120
216 =xy
x=216/y
Now x+y =30
216/y + y =30
multiply by y
216+y^2=30y
y^2-30y+216=0
y^2-18y-12y+216=0
y(y-18)-12(y-18)=0
(y-12)(y-18)=0
y= 12 OR 18
The dimensions of the cardboard are 18 by 12 cm