How did PoShen Loh get 1/16 as the constant?

Module 2 Week 4 Day 16 Bonus Explanation
At 2:20, PoShen Loh explains that you need to multiply a constant (the yellow box at 2:20) with
( a + b + c )( a + b + c)( a  b + c )( a + b  c ). How exactly did he get 1/16 from the 13 14 15 triangle? 
Hi @JerryHuang!
Thanks for asking!
We found out that for any triangle, the following is true:
$$\text{Area}_\triangle^2={\color{orange}\boxed{\text{??}}}\times(a+b+c)(a+b+c)(ab+c)(a+bc)$$ In addition to this, we found, using an absolutely different method, that \(\text{Area} _ {\triangle131415}=84.\)
So, on the one hand, we have$$\text{(Area} _ {\triangle131415})^2=84^2=7056$$ And, on the other hand, we know that $$\text{(Area} _ {\triangle131415})^2={\color{orange}\boxed{\text{??}}}\times(13+14+15)(13+14+15)(1314+15)(13+1415)$$ $$\text{(Area} _ {\triangle131415})^2={\color{orange}\boxed{\text{??}}}\times 42\times 16\times 14\times 12$$ $$84^2={\color{orange}\boxed{\text{??}}}\times 42\times 16\times 14\times 12$$
So now we can find our \({\color{orange}"\text{yellow box}"}\): $${\color{orange}\boxed{\text{??}}}=\frac{84\times 84}{42\times 16\times 14\times 12}=\frac{42\times 2\times 84}{42\times 16\times 168}=\frac{42\times 168}{42\times 16\times 168}={\color{orange}\boxed{\frac{1}{16}}}.$$ 
Ah. Thanks! I didn't think 1/16 would come from solving the equation, but apparently it does!

@JerryHuang I think so if you do all of the soling equations you get 42168/4216*168 which gets you 1/16 which is just only a matter of solving equations!!