Hi, I'm having problems on how to setup this problem. Would appreciate any help.

A gutter is to be made by folding up the edges of a strip of metal. If the metal is 12 in wide and the cross-sectional area of the gutter is to be 16 7/8 in sq, what are the width and depth of the gutter.

I understand that the length of the one side is 12-2x, but I don't know how this helps me.

Thanks
Ryan

2. Hello, Ryan!

A gutter is to be made by folding up the edges of a strip of metal.
If the metal is 12 in wide and the cross-sectional area of the gutter is to be 16 7/8 in sq,
what are the width and depth of the gutter?
Code:
   This is the strip of metal before folding.

: - - - - -12 - - - - - :
*-----*-----------*-----*
:  x  :   12-2x   :  x  :

This is the gutter after folding.

*           *
|           |
x |           | x
|           |
*-----------*
12-2x

The cross-sectional area is: . $A \;=\;x(12-2x)$

We're told that this area will be: $16\frac{7}{8} \:=\:\frac{135}{8}$ in².

There is our equation . . . $x(12-2x) \:=\:\frac{135}{8}$

Multiply by 8: . $8x(12-2x) \:=\:135 \quad\Rightarrow\quad 16x^2 - 96x + 135 \:=\:0$

Factor: . $(4x-9)(4x-15) \:=\:0 \quad\Rightarrow\quad x \;=\;\frac{9}{4},\;\frac{15}{4}$

There are two solutions . . .

. . . $\begin{array}{|c|c|}\hline
\text{Height} & \text{Width} \\
x & 12-2x \\ \hline \hline
2.25 & 7.5 \\ \hline \hline
3.75 & 4.5 \\ \hline
\end{array}$

3. I was missing that the height = x. Thanks for the help!