Problema Solution
A rain gutter is made from sheets of aluminum that are 18 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 18-square inches. Show that there are two different solutions to the problem. Round to the nearest tenth of an inch
Answer provided by our tutors
cross-sectional area = height * width
if the width is 'w', then the height is '18-2w', assuming the edges are not curled over
18 = w(18-2w)
solving for 'w' we have w = { 1.145, 7.854 }
18 - 2*1.145 = 15.71
18 - 2*7.854 = 2.292
the two solutions depend on how deep the gutter is made, one can use either of these approximate width/height combos:
width x height:
1.1 x 15.7
7.9 x 2.3