The length of the enlarged garden is x + 3 + 8 feet, or x + 11 feet. Dividing this into the given area x^2 + 20x + 99 produces the quotient x + 9.
The dimensions of the enlarged garden are (x+11) by (x+9). Note that mult. these 2 factors together produces x^2 + 20x + 99, as expected.
Length of enlarged garden is x+11, whereas the width is x+9. Thus, the difference between length and width of the enlarged garden is 2 feet.