text: I assume you want the values of x and y?\n\nTop triangle hypotenuse:\nsqrt( (y-4)^2 + 16 ) \n\nTop triangle vertical leg:\ny-4\n\nFull triangle hypotenuse:\n12\n\nFull triangle vertical leg:\ny\n\nBy similar triangles\nsqrt( (y-4)^2 + 16 ) / (y-4) = 12 / y\n\nMultiply by (y-4) and y:\ny sqrt( (y-4)^2 + 16 ) = 12 (y-4)\n\nSimplify:\ny sqrt( y^2 - 8y -16 + 16 ) = 12y - 48\ny sqrt( y^2 - 8y ) = 12y - 48\ny sqrt( y (y-8) ) = 12y - 48\n\nSquare both sides:\ny^2 * y(y-8) = (12y - 48)^2\ny^4 - 8y^3 = 144y^2 - 8*144y - 48^2\ny^4 - 8y^3 - 144y^2 + 8*144y + 48^2 = 0\n\nNow just solve for y, and from there it is easy to solve for x...\n\nAfter a bit of playing with an Excel spreadsheet, I'm getting the following pairs:\n\nx = 6.680915, y = 9.968218\nx = 9.968218, y = 6.680915\n\nNotice how these are symetric answer depending on whether x is a long leg or y is a long leg.  Double checking the answers we get:\n\nx^2 + y^2 = 12\nsqrt((x-4)^2 + 4^2) + sqrt((y-4)^2 + 4^2) = 12\n\nThe two solutions are therefore:\nx = 6.680915, y = 9.968218 (y is the long leg)\nx = 9.968218, y = 6.680915 (x is the long leg)\n\nIf you assume y > x, then the first solution is the only solution.