Let

x = the length

y = the breadth (width), y <=x

Since the perimeter is 500 yd we can write:

2x + 2y = 500 divide both sides by 2

x + y = 500/2

x + y = 250

y = 250 - x

The area is 14,400 sq. yds. means:

x*y = 14400

Plug y = 250 - x into the above equation and solved for 'x':

x(250 - x) = 14400

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Click here to see the step by step solution for x

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x1 = 160 yd

x2 = 90 yd

For x =160 yd we find

y = 250 - 160

y = 90 yd 

90 < 160 so this is one solution.

For x = 90 yd we find 

y = 250 - 90

y = 160 yd

160 > 90, it is no a solution since it doesn't satisfy the condition y<=x.

So, the length is 160 yds and the breadth is 90 yds.