SOLUTION: A science museum is going to put an outdoor restaurant along one wall of the museum. The restaurant space will be rectangular. Assume the museum would prefer to maximize the area f

Question 551585: A science museum is going to put an outdoor restaurant along one wall of the museum. The restaurant space will be rectangular. Assume the museum would prefer to maximize the area for the restaurant.
a. Suppose there is 120 feet of fencing available for the three sides that require fencing. Write a quadratic equation for the area of the restaurant in terms of either the length or width of the fencing. (Note: Your equation should contain either the length or the width, not both! Think of how you can rewrite the equation in terms of just one of these variables using the perimeter.)
b. In order to maximize the area, what will be the length of the longest side of fencing?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a. Suppose there is 120 feet of fencing available for the three sides that require fencing.
Write a quadratic equation for the area of the restaurant in terms of either the length or width of the fencing.
Let L = the length of the fenced area
Let x = the width
:
Three sides so the perimeter:
L + 2x = 120
L = (120-2x);
:
Area = L * x
Replace L with (120-2x)
A = x(120-2x)
A = -2x^2 + 120x; a quadratic equation representing the area
:
:
b In order to maximize the area, what will be the length of the longest side of fencing?
Max area occurs at the axis of symmetry, x = -b/(2a); a=-2; b= 120
x =
x = +30 ft is the width for max area
Find the Length
L = 120 - 2(30)
L = 60 ft is the length for max area
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