Question

I have snapped a picture of the question I am needing help with. Thank you.

Answer 1

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:

`l=w+20`

The volume is determined as

`V=l* w* h`

Substitute the values

`\begin{gathered} 2304=(w+20)* w*4 \\ 2304=(w^2+20w)4 \\ 2304=4w^2+80w \\ 4w^2+80w-2304=0 \end{gathered}`

Solve the quadratic equation.

`\begin{gathered} (w-16)(w+6)=0 \\ w=16,-6 \end{gathered}`

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.