SOLUTION: The lengths of the sides of a triangle are 2, 5, and x cm; and the area is x square cm. compute the numerical value of x

Heron's formula for the area A of a triangle with
sides a,b, and c is

 where 

So we have a=2, b=5, and c=x and A = x.

We will eventually let , , ,
and 

But to make things easier we will first simplify
Heron's formula by first removing the square root and
secondly, eliminating s:





where





so, substituting to eliminate s,









Now that we have rewritten Heron's formula in terms of the
sides only, we simplify the factors to substitute in
the above revised version of Heron's formula, which I think
is superior to the original version, especially for 
calculating purposes.

So now we substitute , , , and 







Substituting these factors:















That factors as



So 

and 

Edwin