For the given figure:
the dimensions of the sheet are: 28 inches and 16 inches
We will cut 4 squares from the corner, each square of side length = x
Folding up the sides, we will give us a box with the following dimensions:
Length = 28 - 2x
Width = 16 -2x
Height = x
the volume of the box = Length * width * height
So,
[tex]V(x)=x(28-2x)\cdot(16-2x)[/tex]
we will find the values of (x) which make V(x) = 0
so,
[tex]\begin{gathered} x(28-2x)(16-2x)=0 \\ x=0 \\ or,28-2x=0\rightarrow x=\frac{28}{2}=14 \\ or,16-2x=0\rightarrow x=\frac{16}{2}=8 \end{gathered}[/tex]
The possible values will be x = 0 or 8
x = 14 is not possible because it will not be achievable
on the side of length 16
so, the answer will be x = 0, 8
