A rain gutter is to be made of aluminum sheets that are 28 inches wide by turning up the edges 90degrees. What depths will allow at least 66 square inches of water to flow?

d=4inches

Or d=10 inches

Step-by-step explanation:

Let d = depth of gutters

Let 28 - d be width of gutters

Cross sectional area of gutter = d (28-2d)

66 = d (28-2d)

66 = 28d - 2d^2

2d^2 - 28d + 66=0

Dividing by 2 gives

d^2 - 14d + 33

Using Almighty formular

d = - (-14) + - sqrt ( - (-14) - (4*1*33) / 2

d = 14+-sqrt (196-132) / 2

d = 14+-sqrt (64) / 2

d = 14 + - (8/2)

d=14+-4

d=14+4=18 or

d = 14-4=10