Answer
The length is $11$, the width is $13$.
Work Step by Step
Let the width of the window be $x$, then the length of it is $x+2$, then our equation for the area is: $x(x+2)=143\\x^2+2x=143\\x^2+2x-143=0\\x^2-11x+13x-143=0\\x(x-1)+13(x-11)=0\\(x-11)(x+13)=0$
Thus $x=11$ or $x=-13$, but $x=-13$ doesn't make sense, thus the length is $11$, the width is $13$
