Max Word
2010
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Max Word

Max area word problem?
Here is the word problem I have:
A lifeguard marks off a rectangular swimming area at a beach with 200 m of rope. What is the greatest area of water she can enclose?
Here's what I've done so far:
Let l be length.
Let w be width.
2l + 2w = 200
Then, I isolated "l" to get:
l = 100 - w
Then, I subbed "l" into area = l x w to get:
(100-w)(w)
= -w^2 + 100w
Then I completed the square.
= -(w^2 + 100w + 2500 - 2500)
= -(w+50)^2 + 2500
The answer in my textbook says the max. area is 5000 m^2. Why isn't the max area 2500? (As stated in my equation).
If you want a rectangular shape with the largest area, then the best shape is a square if they must have the same perimiter. Therefore, I'd say:
50x50
= 2500m^2


US $73.00



















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