The equation $x^2 - x - 12 = 0$ comes from a rectangle of area $12$ sq. cm. with breadth $(x - 1)$ cm and length—

For a rectangle, area $=$ length $\times$ breadth. Since breadth $=(x-1)$ and area $=12$, the equation $x^2-x-12=0$ expands from $(x)(x-1)=12$, so the length must be $x$ cm.