Question 1060643
.
An open-topped box can be created by cutting congruent squares from each of the four corners of a piece of cardboard 
that has dimensions of 20 cm by 30 cm and folding up the sides. Determine the dimensions of the squares that must be cut 
to create a box with a volume of 1008cm^3.
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<pre>
(20-2x)*(30-2x)*x = 1008.

{{{(600 - 60x - 40x + 4x^2)*x}}} = 1008,

{{{(4x^2 - 100x + 600)*x}}} = 1008,

{{{(x^2 - 25x + 150)*x}}} = 252,

{{{x^3 - 25x^2 + 150x - 252}}} = 0,


One root is x= 3.


So, one solution is x= 3.


Two others are  x= {{{11-sqrt(37)}}} =~ 4.92  and  x= {{{11+sqrt(37)}}} =~ 17.08. The latest is TOOOOO big.


<U>Check</U>.  (20-2*3)*(30-2*3)*3 = 14*24*3 = 1008.


<U>Answer</U>.  One solution is x= 3.  Another is  x= {{{11-sqrt(37)}}} =~ 4.92


{{{graph( 330, 330, -2.5, 20.5, -80.5, 20.5,
          x^3 - 25x^2 + 150x - 252
)}}}


Plot y = {{{x^3 - 25x^2 + 150x - 252}}}
</pre>