Question 1093433
<br>Let x be the side length of the square box that is being constructed.  Since squares of length 55 feet are cut out of each corner of the original piece of sheet metal, the side length of the original piece of metal is x+110.<br>
The volume of the box, given as 605605 cubic feet, is 55x^2.  So<br>
{{{55x^2 = 605605 = 605*1001 = 55*11*7*11*13}}}
{{{x^2 = 11*11*7*13}}}
{{{x = 11*sqrt(91)}}}<br>
So the length of the side of the original piece of metal is<br>
{{{11*sqrt(91)+110}}}