Let the area of the largest rectagle be A, the blank rectangle cut out be B, and the shaded shape of letter "L" be C. Thus, we have: A-B=C Here, C=6, so A-B=6 From the diagram, we have: A=x(x+1) and B=2x So, the equation, A-B=6, can be rewritten: x(x+1)-2x=6 Simplify the equation,getting x^2-x-6=0 Factor the equation,getting (x-3)(x+2)=0 From the diagram, x>2 so x+2≠0 Thus, we have: x-3=0 That is: x=3 The answer is: x=3