Problem 5, 2018

Three squares are inscribed in a right triangle \(ABC\) with the right angle at \(B\), arranged as in the picture: the largest one has two sides lying on the legs of the triangle, and each of the two smaller ones is wedged between the largest square and a leg. Every one of the three squares has a vertex on the hypotenuse \(AC\). The two smaller squares have sides of length \(3\) and \(4\). Compute the length of \(AC\).