Question 343889
The area of a rectangle is,
1.{{{A=L*W=5000}}}
The perimeter of a rectangle is,
{{{P=2L+2W=300}}}
2.{{{L+W=150}}}
From eq. 1,
{{{L=5000/W}}}
Substitute into eq. 2,
{{{5000/W+W=150}}}
{{{5000+W^2=150W}}}
{{{W^2-150W+5000=0}}}
{{{(W-100)(W-50)=0}}}
Two solutions:
{{{W-100=0}}}
{{{W=100}}}
Then 
{{{L=5000/W=50}}}
.
.
.
{{{W-50=0}}}
{{{W=50}}}
Then
{{{L=5000/50=100}}}
.
.
.
The field is 50m x 100m.