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If each side of the play area is 7x + 8 feet long and x = 25 feet, then each side of the play area is 7(25) + 8 = 175 + 8 = <<7*25+8=183>>183 feet long.
Since a pentagon has 5 sides, the perimeter of Sandy's school playground is 183 * 5 = <<183*5=915>>915 feet. Answer: \boxed{915}.