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
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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?
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
