Question 93421
Put the intersection on the origin of an xy coordinate system.
Mark the point (600,0) on the x axis.
Mark the point (0,400) on the y axis.
Draw a line thru those two points. 
That line is the railroad track.
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Find the equation of that line using the two points.
You get slope = -400/600 = -2/3
You have the y-intercept at 400
The equation is y = (-2/3)x+400
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Sketch a rectangle inside the figure touching the railroad line at (x,y),
with other vertices, (0,0), (0,y), (x,0)
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The area of that rectangle is x*y
A = xy
But y = (-2/3)x+400, so you get
A = x[(-2/3)x+400]
A = (-2/3)x^2 + 400x
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The maximum value for A occurs when x = -b/2a
x = -(400/[2(-2/3)]
x = 200/(2/3)
x = 300
Substitute that into y = (-2/3)x + 400 to get:
y = (-2/3)*300 + 400
y = -200 + 400
y = 200
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The dimensions of the rectangle with maximum area are 300 by 200
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Cheers,
Stan H.