SOLUTION: Ana has 40 ft of fencing materials to be used for three sides of a rectangular garden, while a wall serves as her fourth side. What measures of the width will give an area of at l

Question 1171624: Ana has 40 ft of fencing materials to be used for three sides of a rectangular garden, while a wall serves as her fourth side. What measures of the width will give an area of at least 150square ft?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Ana has 40 ft of fencing materials to be used for three sides of a rectangular garden, while a wall serves as her fourth side.
What measures of the width will give an area of at least 150 square ft
:
L + 2w = 40
L = 40 - 2w
:
The area
L * w = 150
replace L with (40-2w)
(40-2w)*w = 150
40w - 2w^2 = 150
Arrange as a quadratic equation
-2w^2 + 40w - 150 = 0
simplify, divide by -2
w^2 - 20w + 75 = 0
factors to:
(w-5)(w-15) = 0
Two solutions
w = 5 ft, then L = 30 ft
and
w = 15 ft, then L = 10 ft

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