# Math Help - A word Problem

1. ## A word Problem

Hi, I'm new here. Nobody in my pr-calc class could figure out how to do this problem, so hopefully you can.

Calvin wants to make a gutter with a rectangular cross section by folding up strips of equal width on a long sheet of metal that is 26cm wide. The larger the cross sectional dimensions, the greater the capacity of the gutter. Find the dimensions that will maximize the gutter's capacity.

Thanks!

2. You can do with or without calculus.

Without calculus method:

Let the lengths of the folded up sides be x.

Then the base will have width 26-2x

The area of the gutter is $x(26-2x) = -2x^{2}+26x$

Now you have a quadratic to solve.

To find the maximum capacity of the gutter, use x = -b/(2a).