Given :
The length of the metal is 20 inches longer than the width.
But we fold up 4-inch flaps on each side, so the height of the box is 4 inches, and the length and width will each decrease by 8 inches (4 inches on each side). Since the length and width decrease by the same amount, the length will still be 20 inches longer than the width.
Explanation :
So the equations would be:
[tex]l=w+20[/tex]
The volume is determined as
[tex]V=l\times w\times h[/tex]
Substitute the values
[tex]\begin{gathered} 2304=(w+20)\times w\times4 \\ 2304=(w^2+20w)4 \\ 2304=4w^2+80w \\ 4w^2+80w-2304=0 \end{gathered}[/tex]
Solve the quadratic equation.
[tex]\begin{gathered} (w-16)(w+6)=0 \\ w=16,-6 \end{gathered}[/tex]
Since the width can't be negative, the width of the box is 16 and the length is l= (16 + 20)=36.
But remember, the length and width of the piece of metal are each 8 inches longer than the box, so it was 24 inches by 44 inches.
