For this expression "a rectangle is 6 cm longer than it is wide"

First let w stands for the width of the rectangle.  And let x stands for the original area of the rectangle.

lenth = w + 6

Area = length x width

x = (w + 6) (w)

Now for this statement: If the length and the width are both increased by 3 cm, the area is increased by 99 cm squared. Find the original dimensions.

(w + 6) (w) = Area

(w + 6 + 3) (w + 3) = (w + 6) (w) + 99

(w+9)(w+3) = w2 + 6w +99

w2 + 3w + 9w + 27 = w2 + 6w +99

w2 + 12w + 27 = w2 + 6w +99

w2 - w2 + 12w - 6w =99-27

6w =72

w=72/6

w = 12cm

So the original width of the rectangle is 12cm, its length is said to be 6 cm longer that its wide which is expressed as:

lenth = w + 6

length = 12 + 6

length = 18cm

Checking:

Original Area:

lxw =A

18 x 12 = 216cm

When both of the dimension is increased by 3, the area also increased by 99

Original Area = 216cm

(18+3)(12+3) = A + 99

(21)(15) = 216 +99

315=315