A right angled triangle has sides of length X, Y and Z (all lengths in cm.). It is known that Z is the length of the longest side.
The lengths of the other two sides satisfy the inequality $\sqrt{x^2-4\sqrt{2}x + 12} + \sqrt{y^2-6\sqrt{3}y + 31} \leq 4$
What is the length (in cm.) of the hypotenuse of this triangle?
How can we get the exact value of $x$ and $y$? Since during solving equation get in the power of 8 and very complicated.
Thanks in advance.