I drew a diagram and labeled some lengths.
From the diagram
x + 2 y = 48
The triangle in the upper right that is to be cut off is a right triangle and hence from Pythagoras theorem
y2 + y2 = x2
Thus 2 y2 = x2 and √2 y = x. Substituting into the first equation gives
√2 y + 2 y = 48 so y = 48/(√2 + 2) = 14.06 inches or 14 1/16 inches.