This depends on the shape which you are concerned with.
any shape whose area and perimeter calculations require more than 1 variable its perimeter can change depending on the dimensions.
for others that require a single variable it does not affect its perimeter
perimeter of a rectangle=2l+2b
area of a rectangle=lxb
let us assume l*b=k where k is some constant.
if you increase l,you have to decrease b and vice versa.
if area of a rectangle =40sq.cm ,you can have a rectanle with either l=10cm and 4cm or l=20cm and 2 cm.Obviously the perimeter in both the case will be different.
infact u can have many rectangle as long as the satisfy the l*b =k relation.
now take the example of a circle:
it's area =pi*r^2
and perimeter =2*pi*r
it has only one variable and hence its area and perimeter will remain fixed for a particular value of the radius.