Question 388328
Remember the formula for a parabola, y=(x-h)^2+k, with h & k being the coordinates of the vertex.  Put the problem in this form for the area and you got it!

Let x be the long side of the rectangle area, and y the two short sides.
perimeter=120=x+2y
2y=(120-x)
y=(120-x)/2
Area=xy=x(120-x)/2=1/2(120x-x^2)=-1/2(x^2-120x)
because the coefficient is negative, this is a parabola that turns downward
completing the square, -1/2(x^2-120x+3600)+1800 (we are adding (-1800) so we must add (+1800))
=-1/2(x-60)^2+1800
referring to the basic parabola form above, h=60, and k=1800,representing the long side and maximum area respectively.
y=(120-x)/2=(120-60)/2=60/2=30
ans:(a) The long side of the restaurant is 60 feet.
(b)The maximum area of the restaurant is 1800 sq feet.