Pick one of the cross-sections - perhaps the rectangle.

In this challenge, why does it help to think about the cross-section (profile) and not at all about how long the gutter might be?

The material "length" of the profile of the rectangle wasn't specified in the problem - perhaps it doesn't matter or perhaps we need to give it a value and see what happens.

By the end you will have used the idea that this problem is about shape and not about size.

What did your answers tell you about the "best shape" for the profile?

The picture suggests two other shapes to work with, but there are other possibilities, which did you think to try? Did you include a trapezium?