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

for ex:
perimeterĀ 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.

for ex:
if area of a rectangle ,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.