Question 1205671
the total surface of the rectangular piece of cardboard, before cutting, is equal to 16 * 9 = 144 square inches.


if you remove a square of x inches on a side from each corner of the box, the remaining surface area will be 16 * 9 - 4 * x^2 = 144 - 4 * x^2


if the remaining surface area is 128 square inches, then your formula becomes 144 - 4 * x^2 = 128.


add 4 * x^2 to both sides and subtract 128 from both sides of the equation to get 144 - 128 = 4 * x^2 which simplifies to 16 = 4 * x^2 which simplifies further to 4 = x^2.


solve for x to get x = 2.


the length will be 16 minus 2 * 2 = 12
the width will be 9 minus 2 * 2 = 5
the height will be 2.


the area of the bottom of the box will be 12 * 5 = 60
the area of the 2 vertical sides along the length will be 12 * 2 = 24 each for a total area of 48.
the area of the 2 vertical sides along the width will be 5 * 2 = 10 each for a total area of 20.


the total surface area of the box will be 60 + 48 + 20 = 128 square inches.