Question 353118
<pre>
{{{drawing(400,275,-16,16,-11,11, rectangle(-15,-10,0,10),
 rectangle(0,-10,15,10), locate(-15+.2,0,h), locate(0+.2,0,h), locate(15+.2,0,h), locate(7.5,10,x), locate(-7.5,10,x), locate(7.5,-10,x), locate(-7.5,-10,x)


  )}}}
 
Let the area be {{{y}}}

Area = (base)(height)

Base = {{{2x}}}
Height = {{{h}}}

Let the area be {{{y}}}

{{{y = 2xh}}}

Sum of fencings = {{{4x + 3h}}}

{{{4x + 3h = 120}}}
     
Solve for h

{{{3h = 120 - 4x}}}

{{{h = (120-4x)/3}}}

{{{h = 120/3 - expr(4/3)x}}}

Substitute in

{{{y = 2xh}}}

{{{y = 2x(120/3 - expr(4/3)x)}}}

{{{y = expr(240/3)x - expr(8/3)x^2)}}}

{{{y = 80x - expr(8/3)x^2)}}}

{{{y = -expr(8/3)x^2 + 80x}}}

Use the vertex formula for this parabola:

{{{graph(400,400,-5,35,-50,700, 80x -(8/3)*x^2)}}}

x-coordinate of vertex = {{{-b/(2a)=(-80)/(2*(-8/3))=(-80)/(-16/3)=-80*(-3/16)=15}}}

{{{h = (120-4x)/3}}}
{{{h = (120-4*15)/3}}}
{{{h = (120-60)/3}}}
{{{h = 60/3}}}
{{{h = 20}}}

So the dimensions are 2x by h or 2(15) by 20 or 

30ft by 20ft.

{{{drawing(400,275,-16,16,-11,11, rectangle(-15,-10,0,10),
 rectangle(0,-10,15,10), locate(-15+.2,0,20), locate(0+.2,0,20), locate(15+.2,0,20), locate(7.5,10,15), locate(-7.5,10,15), locate(7.5,-10,15), locate(-7.5,-10,15)


  )}}}

Edwin</pre>