SOLUTION: A determined gardener has 100 ft of deer-resistant fence. She wants to enclose a rectangular vegetable garden in her backyard, and she wants the area that is enclosed to be at leas

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Question 1106148: A determined gardener has 100 ft of deer-resistant fence. She wants to enclose a rectangular vegetable garden in her backyard, and she wants the area that is enclosed to be at least 600 ft2. What range of values (in ft) is possible for the length of her garden? (Enter your answer using interval notation.)

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x is the length
50-x is the width
This way the perimeter, 2L+2W=2x+100-2x=100 feet
x(50-x) is the area.
-x^2+50x=600
-x^2+50x-600=0
vertex is at -50/-2=25
f(25)=625
the zero points occur when x^2-50x+600=0 (changing signs of the left side)
that factors into (x-30)(x-20)=0
x=20, 30 for critical values where the area is 600
20<=x<=30 feet for length.

graph%28300%2C300%2C-10%2C60%2C-200%2C100%2C-x%5E2%2B50x-600%29