SOLUTION: A Gardener wants to fence a 350 square foot rectangular garden into 3 equal sections with fencing parallel to one of the sides of the rectangle. The total length of the garden area

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Question 922034: A Gardener wants to fence a 350 square foot rectangular garden into 3 equal sections with fencing parallel to one of the sides of the rectangle. The total length of the garden area is 15 feet longer than twice its width. How much fencing should she purchase?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The measurements of the rectangular garden are
x= width, in feet, and 2x%2B15= length in feet.
.
The area of that garden in square feet is
x%282x%2B15%29=350
2x%5E2%2B15x=350
2x%5E2%2B15x-350=0
We can easily solve this equation by factoring or by using the quadratic formula.
I prefer factoring.
Looking for factors of 2%2A%28-350%29=-700 that add up to 15 ,
I find that 35%2A%28-20%29=-700 and 35%2B%28-20%29=15 .
2x%5E2%2B15x-350=0--->2x%5E2-20x%2B35x-350=0--->2x%28x-10%29%2B35%28x-10%29=0--->%282x%2B35%29%28x-10%29=0--->system%28x=10%2C%22or%22%2Cx=-35%2F2%29
As x is a measure of the width of the garden, in feet, x=10 is the only acceptable solution.
So the width is 10 feet,
and since 2%2A10%2B15=35 ,
the length is 35 feet.
The best way to split the garden in 3 sections is with fencing sections parallel to the short sides:
.
From the drawing, I see that the gardener needs to set up fencing along the two 35-foot length and along the 4 10-foot sections.
The gardener needs
4%2A10ft%2B2%2A35ft=40ft%2B70ft=highlight%28110ft%29 of fencing.