so if we look at the cross section
and assume that the amount turned up is the same on both sides
so what we can do is make 1 equation and find the max or vertex
if the sides are legnth x and base is y
2x+y=18
and the cross sectional area is xy
2x+y=18
minus 2x both sides
y=18-2x
sub for y
x(18-2x)=areamax
18x-2x^2=areamax
we have a parabola
-2x^2+18x+0=areamax
to find the max y valie or area, we find the y value of the vertex
but the x value of the vertex is what we are looking for to find the value of x to max the area
for
ax^2+bx+c=y
x value of vertex is -b/2a
-18/2(-2)=-18/-4=9/2=4.5
4.5=x value of vertex
aswer is 4.5in
C is answer
