Question

Help with a word problem..

Answer 1

A rain gutter is made from sheets of aluminum that are 24 inches wide. The edges are turned up to form right angles. Determine the depth of the gutter that will allow a cross-sectional area of 58 square inches. There are two solutions to this problem. Round to the nearest tenth of an inch.

Answer 2

A rain gutter is made from sheets of aluminum that are 24 inches wide. The edges are turned up to form right angles. Determine the depth of the gutter that will allow a cross-sectional area of 58 square inches. There are two solutions to this problem. Round to the nearest tenth of an inch.

Answer 3

A rain gutter is made from sheets of aluminum that are 20 inches wide.
The edges are turned up to form right angles. Determine the depth of the gutter
that will allow a cross-sectional area of 13 square inches.
Show that there are two different solutions to the problem.
Round to the nearest tenth of an inch.
:
Let x = the depth of the gutter
Let y = the width of the gutter
:
This may illustrate an end view of the gutter: x|_y_|x
then
2x + y = 20 in; the width of the sheets of aluminum
y = (20-2x); use this form for substitution
and
x*y = 13 sq/in; (the cross sectional area of the end of the gutter)
:
Using the area equation replace y with (20-2x)
x*(20-2x) = 13
a quadratic equation
-2x^2 + 20x - 13 = 0

Answer 4

I got to..
-20+- square root 296 over -4