The length of a rectangle exceeds its width by 12 inches and the area is 85 square inches. what are the length and width of the rectangle?

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 .  Bring that 85 over to the other side by subtraction and set the polynomial equal to 0 so we can factor it. .  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!