• Sep 26th 2008, 03:42 PM
rjw_24
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
• Sep 26th 2008, 04:58 PM
Soroban
Hello, Ryan!

Quote:

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: $16\frac{7}{8} \:=\:\frac{135}{8}$ inē.

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 . . .

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

• Sep 26th 2008, 05:19 PM
rjw_24
I was missing that the height = x. Thanks for the help!