Find all triangles of which perimeter and area are numerically equal

Find all triangles of which perimeter and area are numerically equal. I have got solution for right angle triangles but not of others

Area = $rs$, where $r=\text{inradius}$ and $s=\text{perimeter}/2$

You can see that $rs=p \implies r=2$

There are infinite triangles with inradius as $2$

The area is $A = \sqrt{s(s-a)(s-b)(s-c)}$, where $s$ is the semiperimeter. Thus we get $$(a+b+c)^2 = \frac{a+b+c}{2}(\frac{a+b+c}{2} - a)(\frac{a+b+c}{2} - b)(\frac{a+b+c}{2} - c).$$ We can further simplify this to $$16(a+b+c) = (-a+b+c)(a-b+c)(a+b-c).$$ Let $u = -a+b+c$, $v = a-b+c$, $w = a+b-c$. Then $$16(u+v+w) = u v w.$$ In particular any $u,v$ such that $uv > 16$ give a solution for $w$: $$w = \frac{16(u+v)}{uv-16}.$$ Now for such $u,v,w$ we have that $a = \frac{v+w}{2}$, $b = \frac{w+u}{2}$ and $c = \frac{u+v}{2}$ are the sides of a triangle whose area is equal to its perimeter.