What is the perimeter of an isosceles triangle

Depends on the size and shape of it! :)

You can obviously have large triangles and small triangles. The perimeter will definitely change.

You can figure out the perimeter based on the height of the triangle and the dimension of the base. An isosceles triangle has two legs of the same length. If you construct a line from the base of the triangle (the unequal leg) to the apex of the triangle, you form two right triangles. Let's say that the height of the triangle is h. The base is b. Therefore, each right triangle has two legs of length h and b/2. The length of the two equal legs is then

Length\,of\,non-unique\,leg = \sqrt {h^2 + \frac {b}{2}^2}

The length of the base is Length\,of\,base = \frac b2

The total perimeter of the triangle is, therefore

Perimeter =\frac b2 + 2\,\sqrt {h^2 + \frac {b}{2}^2}

You can figure out what to do with this or how to simplify it, if possible.