Question 394927
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Hi
Let x and (500-2x) represent the width and length of pen
Question states***
  x(500-2x) = 15625    |area = width*length
solving for x
 500x - 2x^2 = 15625
   2x^2 - 500x + 15625 = 0
{{{x = (500 +- sqrt( 125000 ))/(4) }}}
x =  36.6m and 213.4m (rounding to nearest tenth and tossing out larger solution)
Length of Pen = 500m- 2*36.6m = 426.8m

CHECKING our Answer
426.8m + 36.6m + 36.6m = 500m of fencing    |pen is against his barn wall