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

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.