What’s the length of the new fence?

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)
 
 The length of the new fence is:
 x = 36/5 meters