SOLUTION: A rectangular metal sheet whose length is 12cm longer than its width is crafted into an open box by cutting out 6X6 centimetres squares from each corner,and folding up flaps.if the

Question 1174787: A rectangular metal sheet whose length is 12cm longer than its width is crafted into an open box by cutting out 6X6 centimetres squares from each corner,and folding up flaps.if the volume of the box is 1872 cubic centimetres,find the dimensions of the original metal sheet

Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
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A rectangular metal sheet whose length is 12cm longer than its width is crafted into an open box
by cutting out 6X6 centimetres squares from each corner,and folding up flaps.if the volume of the box
is 1872 cubic centimetres,find the dimensions of the original metal sheet
~~~~~~~~~~~~~~

Let x be the width of the rectangular metal sheet, in centimeters.

then its length is (x+12) cm.



After cutting the 6x6-squares and making the box,

the base of the box has dimensions (x-12) and ((x+12)-12) = x centimeters;

the height of the box is 6 cm, and THEREFORE, the volume equation is


    6x*(x-12) = 1872.


Reduce the factor 6 in both sides


    x*(x-12) = 312.


It is a quadratic equation


    x^2 - 12x - 312 = 0.


Solve it using the quadratic formula.

You have instructions --- it means that you know the way.

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