SOLUTION: a gardener has 120 ft of deer resistant fence. She wants to enclose a rectangular vegetable garden in her backyard, and she wants the area enclosed to be at least 800 ft² what rang

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Question 185086: a gardener has 120 ft of deer resistant fence. She wants to enclose a rectangular vegetable garden in her backyard, and she wants the area enclosed to be at least 800 ft² what range of values is possible for the length of her garden?
please help.
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
A square has the largest area for perimeter length.
120/4=30 length of a side of the square
30^2=900 ft^2 largest area.
.
(30+x)(30-x)=800 Let x be the increase in length (or the decrease in width)
900-x^2=800
-x^2+100=0
x^2-100=0 multiply each side by -1
(x-10)(x+10)=0
x=10
40 x 20 is the longest 800 ft^2 area rectangle that can be built.
.
The longest length is 40 ft and the shortest is 30 ft.
.
Ed