This is an isoperimetric problem for triangles. Of all triangles with the same perimeter, which one has the greatest area? The answer is an equilateral triangle. You've stated it for isosceles triangles, and the proof is a little easier there. read more
The base is the easy part: just use the third, unequal side of the isosceles. For example, if your isosceles triangle has sides of 5 centimeters, 5 cm, and 6 cm, use 6 cm as the base. read more