Question 800108
let w be the width of the rectangle and
w+4 is the length 
w*(w+4) = A, where A is the area of the rectangle,
(w+1)*(w+5) = A+18
from our first equation we have w^2 +4w = A
from our second equation we have w^2 +6w +5 = A +18
now substitute for A in the second equation
w^2 +6w +5 = w^2 +4w +18
now we can subtract w^2 from both sides of the =
6w +5 = 4w +18
subtract 4w from both sides of =
2w = 13
w = 6.5 cm and length is 10.5cm
now check the answer
6.5 * 10.5 = 68.25 cm^2   and
7.5 * 11.5 = 86.25 cm^2
86.25 - 68.25 = 18 cm^2 as required