Atriangular lake-front lot has a perimeter of 1300 feet. one side is 300 feet longer than the shortest side, while the third side is 400 feet longer than the shortest side. find the lengths of all three sides.

a) 200 ft, 500 ft, 600 ft
b) 300 ft, 300 ft, 300 ft
c) 100 ft, 200 ft, 300 ft
d) 300 ft, 600 ft, 700 ft