Question 178715
Thomas is going to make an open-top box by cutting equal squares from the four
 corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides.
 If the area of the base is to be 80 square inches, then what size square should 
be cut from each corner?
:
Let x = side of the square to be cut off
:
Box dimension : (11-2x) by (14-2x) by x
:
Base as given = 80 sq/in, therefore
(11-2x) * (14-2x) = 80
FOIL
154 - 22x - 28x + 4x^2 = 80
:
154 - 50x + 4x^2 - 80 = 0
Arranged as a quadratic equation:
4x^2 - 50x + 74 = 0
Simplify divide by 2
2x^2 - 25x + 37 = 0
Solve this using the quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
in this equation a=2, b=-25, c=37
{{{x = (-(-25) +- sqrt(-25^2 - 4 * 2 * 37 ))/(2*2) }}}
:
{{{x = (25 +- sqrt(625 - 296 ))/(4) }}}
:
{{{x = (25 +- sqrt(329 ))/(4) }}}
Two solutions
{{{x = (25 + 18.14)/(4) }}}
{{{x = 43.14/4}}}
x = 10.785
and
{{{x = (25 - 18.14)/(4) }}}
{{{x = 6.86/4}}}
x = 1.715 inches (the solution that makes sense)
;
:
Check solution
(11-2(1.715)) * (14-2(1.715)) = 
(11-3.43) * (14-3.43) = 80.0