Question 467363
"An open box is to be constructed from 84 square inches of material.
 What should be the dimensions of the base if the height of the box is to be 2 inches? 
Surface Area: S = x^2 + 4xh
height is given as 2", therefore
SA = x^2 + 4x*2
SA = x^2 + 8x
:
The base is square, therefore the material is square
{{{sqrt(84)}}} = 9.165" square
x =  9.165 - 2(2); subtract the 2" used for the 2" height on each side
x = 9.165 - 4
x = 5.165" length and width of the base
Surface area
SA = 5.165^2 + 8(5.165)
SA = 26.677 + 41.32
SA = 68 sq/inches, surface area of the box
:
:
We can check this, 4 each 2" squares removed to accomplish this
Total area of these squares: 4(4) = 16 
Box area plus 2" square areas should = the original material area
68 + 16 = 84
:
:
It just dawned me we could have done this in our head. Given the height is 2" we know that 4 ea 2" squares will be removed for a total of 16 square inches.
What remains, is the surface area of the box, 84-16 = 68 sq/inches!