The area of a rectangle is length (l) * width (w)

l = w + 1

(length is 1 more than width)

We can now write the problem as this:

306 = w(w + 1)

306 = w^2 + w

0 = w^2 + w - 306

We can use the quadratic formula to find the solutions:

0 = (-b +- sqrt(b^2 - 4ac))/2a

The coefficient of w^2 is 1, so a = 1; the coefficient of w is 1, so b = 1; and c = -306.

0 = (-1 +- sqrt(1^2 - 4(1)(-306)))/2(1)

0 = (-1 +- sqrt(1 + 1225))/2

0 = (-1 +- 35)/2

This gives us 17 for one solution:

(-1 + 35)/2

34/2

17

and 18 for the other solution:

(-1 - 35)/2

-36/2

-18

Since the width cannot be negative, the width must be 17.

l = w + 1

l = 17 + 1

l = 18

The length is 18 cm and the width is 17 cm.