Let x denote the length of one leg. Then the perimeter of the triangle is:

That means the triangle has the side length:

a = 12, b = 12, c = 18 (c is the base)

1. Calculate the area by Heron's formula:

The half perimeter is s = 21

2.Theheight of the trinagle. Actually there are (normally) three heights in every triangle. Here 2 of the three heights are equal.

From you get

Plug in the values you know to calculate the heights: