Smallest Scalene Obtuse Triangle with Integer Sides and Area

Theorem
The smallest scalene obtuse triangle with integer sides and area has sides of length $4, 13, 15$.

Proof
From Heron's Formula, the area $A$ of $\triangle ABC$ is given by:
 * $A = \sqrt {s \paren {s - a} \paren {s - b} \paren {s - c} }$

where $s = \dfrac {a + b + c} 2$ is the semiperimeter of $\triangle ABC$.

Here we have:

Thus: