We apply the Pythagorean theorem twice and obtain: 12 ^ 2 = x ^ 2 + (15-d) ^ 2 9 ^ 2 = x ^ 2 + d ^ 2 We observe that it is a system of two equations with two unknowns whose solutions are: (x, d) = (-36/5, 27/5) (x, d) = (36/5, 27/5) We ignore the negative solution, therefore, the solution is: (x, d) = (36/5, 27/5) Answer: The length of the new fence is: x = 36/5 meters
