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Question 619584: Hi, please help me solve the question:
A rectangular sheet of steel is twice a long as it is wide. From each corner a 2 cm-square is cut. Then the sides are folded to make a box (without top), which holds 60 cubic centimeters. What were the original dimensions of the steel sheet?
Thank you!
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A rectangular sheet of steel is twice a long as it is wide. From each corner a 2 cm-square is cut. Then the sides are folded to make a box (without top), which holds 60 cubic centimeters. What were the original dimensions of the steel sheet?
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let x=width of original steel sheet
2x=length of original steel sheet
After making a 2 cm square cut at each corner and folding the sides, you end up with a box of the following dimensions:
width=x-4
length=2x-4
height=2
volume=length*width*height=60 m^3
2(x-4)(2x-4)=60
(x-4)(2x-4)=30
2x^2-12x+16=30
2x^2-12x+14=0
x^2-6x-7=0
(x-7)(x+1)=0
x=-1 (reject, x>0)
or
x=7
2x=14
width of original steel sheet=7 cm
length of original steel sheet=14 cm
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