SOLUTION: a rain gutter is made from sheets of aluminum that are 28 inches wide. The edges are turned up to form right angles. determine the depth of the gutter that will allow a cross secti

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Question 785551: a rain gutter is made from sheets of aluminum that are 28 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 60 square inches. there are two solutions to this problem. round to the nearest tenth of an inch.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
d= depth of the gutter, in inches.
28-2d= width of the gutter, in inches.
Cross sectional area =d%2828-2d%29 square inches.
60=d%2828-2d%29-->60=28d-2d%5E2%29-->2d%5E2-28d%2B60=0%29-->d%5E2-14d%2B30=0%29
That equation has 2 solutions that can be found either "completing the square or applying the quadratic formula.
The solutions are:
d=7-sqrt%2819%29 approximately highlight%282.64inches%29, and
d=7%2Bsqrt%2819%29 approximately highlight%2811.36inches%29

COMPLETING THE SQUARE:
d%5E2-14d%2B30=0%29-->d%5E2-14d=-30%29-->d%5E2-14d%2B49=-30%2B49%29-->%28d-7%29%5E2=19%29-->d=7+%2B-+sqrt%2819%29

USING THE QUADRATIC FORMULA:
d=+%28-%28-14%29+%2B-+sqrt%28%28-14%29%5E2-4%2A1%2A30+%29%29%2F%282%2A1%29
d=%2814+%2B-+sqrt%28196-120+%29%29%2F2
d=%2814+%2B-+sqrt%2876%29%29%2F2
d=%282%2A7+%2B-+sqrt%284%2A19%29%29%2F2
d=%282%2A7+%2B-+sqrt%284%29%2Asqrt%2819%29%29%2F2
d=%282%2A7+%2B-+2sqrt%2819%29%29%2F2
d=2%287+%2B-+sqrt%2819%29%29%2F2
d=7+%2B-+sqrt%2819%29