SOLUTION: The Height of a box is 2 cm less than the width. the length is 3 less than the width. the volume is 50 cm^3. what are the dimensions of the box?

Question 852226: The Height of a box is 2 cm less than the width. the length is 3 less than the width. the volume is 50 cm^3. what are the dimensions of the box?
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
set W = width , H = height , L = length
H = W - 2
L = W - 3
Since Volume = L*W*H
50 = L*W*H
Substitute W - 2 for H , W - 3 for L
50 = (W - 3)(W)(W - 2)
50 = (W^2 - 3W)(W - 2)
50 = W^3 - 2W^2 - 3W^2 + 6W
50 = W^3 - 5W^2 + 6W
add -50 to each side
0 = W^3 - 5W^2 + 6W - 50
W = 5.54 using www.wolframalpha.com solver
H = 5.54 - 2 = 3.54
L = 5.54 - 3 = 2.54
Testing our solution 5.54*3.54*2.54 = 49.81

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