A triangle has three different integer side lengths

A triangle has three different integer side lengths and a perimeter of 20 units. What is the maximum area of the triangle?

sides are 5, 7, 8       area = 17.321 sq units

The maximum area would be that of an isosceles triangle with sides, 7, 7 and 6. Using Heron's Formula we get the area =18.974 units^2