SOLUTION: A lifeguard is interested in enclosing a rectangular swimming area along the beach. The swimming area will be enclosed using 72m of floating rope and will be bordered on one side b

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Question 737399: A lifeguard is interested in enclosing a rectangular swimming area along the beach. The swimming area will be enclosed using 72m of floating rope and will be bordered on one side by the beach: that is the problem
these are the questions
a. Draw a sketch to model the situation
b. Find the dimensions (length and width) that provide the maximum area for swimming.
c. What is the maximum area available for swimming?
Please could someone help me with this today
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A lifeguard is interested in enclosing a rectangular swimming area along the beach.
The swimming area will be enclosed using 72m of floating rope and will be bordered on one side by the beach: that is the problem these are the questions
:
a. Draw a sketch to model the situation
I'll let you handle this
:
b. Find the dimensions (length and width) that provide the maximum area for swimming.
Only 3 sides are required therefore
L + 2W = 72
L = (72-2W)
:
c. What is the maximum area available for swimming?
A = L * W
Replace L with (72-2W)
A = W(72-2W)
A quadratic equation
A = -2W^2 + 72W
Max area occurs on the axis of symmetry, find it using formula: x = -b/(2a)
W =
W = 18 m is the width that gives max area
then
L = 72 - 2(18) = 36 m is the length for max area
:
Actual max area: 18 * 36 = 648 sq/m
:
:
If you graph the equation you can see that max area occurs when x=18 (width)