Answer
$18$ inches
Work Step by Step
We have a square aluminum sheet, which means each side will be of equal length.
After the small $4$-inch squares are cut out from each corner, the sheet is folded up. This means that a cuboid shape has formed, not a cube, as the height of the shape is different from the length and width.
We know that the formula for the volume of a cuboid is
Length $\times$ Width $\times$ Height
We also know that:
Volume of shape = $400$ $in^3$
Length = $x$
Width = $x$
Height = $4$ (The height is 4 inches as the sides are each $4$ inches tall when folded)
So, we can substitute these values into the formula to find a quadratic equation!
Volume = Length $\times$ Width $\times$ Height
$400 = x \times x \times 4$
$400 = 4x^2$
In this case, we can simply divide each side by 4 and then square root both sides to find the solutions for $x$.
$x^2=\frac{400}{4}$
$x^2=100$
$x= \sqrt {100}$
$x= ±10$ (As we are square rooting, the answer can either be negative or positive, hence the ± sign)
However, in this case, we can discard the negative solution as we are looking for the dimensions of an aluminum sheet, which cannot be below 0.
The original size can be given by the expression $(x+8)$ inches.
Original size =$(10)+8$
$=18$ inches
