Question 551585
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 = {{{(-120)/(2*-2)}}}
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