Problem D

The Largest Square

Three squares are placed side by side with the smallest square on the left and the largest square on the right. The bottom sides of the three squares form a horizontal line.

The side length of the smallest square is \(5\) units, and the side length of the medium-sized square is \(8\) units. If the top-left corner of each square all lie on a straight line, determine the side length of the largest square.