The area of an obtuse triangle with the longest side length equal to 10 cannot equal to 25.5 Need to prove that the area of an obtuse triangle with the longest side length equal to 10 cannot be equal to 25.5

Le $AB$ be the longest side: assume that the origin is the midpoint of $AB$ and $AB$ is oriented like the $x$-axis. Since $\widehat{BCA}>\frac{\pi}{2}$, the vertex $C$ belongs to the half-circle: $$ \\{(x,y)\in\mathbb{R}^2:x^2+y^2<25, y>0\\}$$ hence the distance from the $AB$-side is less than $5$ and the area is less than $\frac{10\cdot 5}{2}=25$.