A city is preparing to mark out two plots to form two new parks. The first park will be in the shape of a right triangle whose sides have the same length, denoted y. The second park will be in the shape of a square, and the length of each side is denoted x. The parks will be fenced, except one side of each park which is bounded by a river. The town has 3400 feet of fencing, and the Director has decided to use all of the fencing and configure the total areas of the parks to be as small as possible. Determine the dimensions, x and y, in feet, that will result in the smallest possible combined area.