SOLUTION: A farmer has a rectangular garden plot surrounded by 120ft of fence. Find the length and width of the garden if its area is 800 square feet.

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Question 399521: A farmer has a rectangular garden plot surrounded by 120ft of fence. Find the length and width of the garden if its area is 800 square feet.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width = w ft
The length will be 800%2Fw ft
Also,
2w+%2B+2%2A%28800%2Fw%29+=+120 ft
Multiply both sides by w
2w%5E2+%2B+1600+=+120w
2w%5E2+-+120w+%2B+1600+=+0
w%5E2+-+60w+%2B+800+=+0
I can solve by completing the square:
w%5E2+-+60w+%2B+%2860%2F2%29%5E2+=+-800+%2B+%2860%2F2%29%5E2
w%5E2+-+60w+%2B+900+=+-800+%2B+900
Both sides are perfect squares
%28w+-+30%29%5E2+=+10%5E2
Take the square root of both sides
w+-+30+=+10
w+=+40
There is a negative root also:
w+-+30+=+-10
w+=+20
The length is 40 and the width is 20
check:
2%2A40+%2B+2%2A20+=+80+%2B+40
80+%2B+40+=+120 OK
area+=+40%2A20+=+800 ft2
OK