If the length exceeds the width by 12, that only means that the length is 12 inches longer. L = w + 12. Width is just w. To find the area we multiply length by width. Since we have a value for the area, our equation looks like this: 85=(w+12)(w). Distributing we have [tex]w^2+12w=85[/tex]. Bring that 85 over to the other side by subtraction and set the polynomial equal to 0 so we can factor it. [tex]w^2+12w-85=0[/tex]. We need to factor that to solve for w. Plugging those numbers into the quadratic formula we get w values of 5 and -17. We all know that the 2 things in math that will never EVER be negative are time and distance/length, so -17 is out. The width then is 5. The length is w + 12, so the length is 17. There you go!
