Morgoth wrote:Two squares of each 5 inches are taken out from the corner.
Therefore minimum length of the original cardboard is 5+5 = 10
You can eliminate all the options except C and D.
Great start, but remember that B is also > 10. We can narrow it down to C and D because we know that the length is 5 + 5 + length of the base of the box, so the answer should be in the form 10 + something.
Now we go 1 step further.
We know that the height of our open box is 5, since we lifted a flap of length 5 to form the outside of the box.
We also know that the base of the box is a square, since we started with a square and cut away the same amount from each dimension.
So, we know that our box has height 5 and length and width x.
Accordingly:
5(x^2) = 40
x^2 = 8
x = root8 = 2root2
So, the length of a side of the original square is:
5 (that we lifted up) + 2root2 (what's left on the base) + 5 (that we lifted up)
= 10 + 2root2
choose (C).
Note that letting x be the base of the box instead of the original length of the cardboard makes the math simpler.
