Question 1052270
The sides will be equal
Let {{{ x }}} = the length of a side of the 
square piece of sheet metal in cm before
the corners are cut out.
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The sides after cutting out corners:
{{{ x - 2*9 = x = 18 }}} cm
The area of the bottom is:
{{{ ( x - 18 )^2 }}}
The volume of the open box is:
{{{ 9*( x - 18 )^2 }}}
{{{ 9*( x^2 - 36x + 324 ) = 144 }}}
{{{ x^2 - 36x + 324 = 16 }}}
Complete the square
{{{ x^2 - 36x = - 308 }}}
{{{ x^2 - 36x + (36/2)^2 = (36/2)^2 - 308 }}}
{{{ x^2 - 36x + 324 = 324 - 308 }}}
{{{ ( x - 18 )^2 = 4^2 }}}
{{{ x - 18 = 4 }}}
{{{ x = 22 }}}
The sheet metal should be 22 x 22 cm2
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check:
{{{ 9*( x^2 - 36x + 324 ) = 144 }}}
{{{ 9*( 22^2 - 36*22 + 324 ) = 144 }}}
{{{ 484 - 792 + 324 = 16 }}}
{{{ 808 - 792 = 16 }}}
{{{ 16 = 16 }}}
OK