Question

A rain gutter is made from sheets of

aluminum that are 14 inches wide by
turning up the edges to form right
angles. Determine the depth of the
gutter that will maximize its cross-
sectional area and allow the greatest
amount of water to flow. What is the
maximum cross-sectional area?

Answer 1

Step-by-step explanation:

Let x = depth of the gutter

then

14-2x = width of the gutter

:

Cross section area:

A = depth * width

A = x(14-2x)

A = 14x - 2x^2

:

Axis of symmetry will give x value for max area: x = -b/(2a)

x = -14/2 * -2

x = -14/-4

x = +3.5 inches is the depth for max area

:

:

Max area: 3.5 * 9 = 31.5 sq/in