Question 1162624
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From the condition, you have this equation


    x + (x+400) + (x + 500) = 1500 feet,


where x is the length of the shortest side.


From this equation


    x = {{{(1500 - 400-500)/3}}} = 200  feet.


Thus the sides are  200 ft, 200+400 = 600 ft  and  200+500 = 700 ft.


The triangle inequalities are hold, so such a triangle does exist.


<U>ANSWER</U>.  The sides are  200 ft,  600 ft  and  700 ft.
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Solved.