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:
 * $A = \sqrt{s \left({s - a}\right) \left({s - b}\right) \left({s - c}\right)}$

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

Here we have:

Thus: