Question 159823
Let x=the sides of the square piece of cardboard.
Cutting a 2 in. square out of each corner leaves the base measurements:
(x-4)^2=x^2-8x+16
The height is 2 in.
volume=2(x^2-8x+16)
84.5=2x^2-16x+32
2x^2-16x+32-84.5=0
2x^2-16x-52.5=0
(x-10.5)(x+2.5)=0
x-10.5=0
x=10.5 inches is the original side of the piece of square cardboard.
Proof:
84.5=2(10.5^2-8*10.5+16)
84.5=2(110.25-84+16)
84.5=2*42.25
84.5=84.5