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A rectangular piece of metal is 20 in longer than it is wide. Squares with sides 4 in long are cut from the four coners and the flaps are folded upward to form an open box. If the volume of the box is 1904 in^3, what were the original dimensions of the piece of metal?

 

What is the width?   in

What is the original length?    in

yojaymarojas  May 13, 2017
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Let the original width be  = W

And the original length = W + 20

 

When the squares are cut  the   dimensions of the box  = (W - 8) in, (W + 20 - 8) in and 4 in

 

And we have that

 

(W - 8) ( W + 20 - 8) (4)  =  1903

 

(W - 8) ( W + 12) (4)  =  1903     simplify

 

4W^2  + 16W - 384 = 1903

 

4W^2 + 16W - 2287  = 0

 

Using the quadratic formula to solve this ( and taking the positive answer) the  solution is that W ≈ 21.995 in 

 

And the length  ≈  21.995 + 20 ≈  41.995 in

 

 

 

cool cool cool

CPhill  May 14, 2017

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