Question

How do you use Heron's formula to find the area of a triangle with sides of lengths `12`, `5`, and `7`?

Answer 1

The given numbers cannot be lengths of sides of a triangle. (The area is zero)

Explanation:

The Heron's formula says that for any triangle with sides `a,b,c` its area is `A=sqrt(p(p-a)(p-b)(p-c))`, where `p=(a+b+c)/2`

If we substitute given numbers we see, that:

`p=(12+5+7)/2=12`, so

`A=sqrt(12*0*7*5)=0`

You should have noticed, that given numbers cannot be the lengths of sides of a triangle, because `12=7+5` and according to triangle inequalities each side must be smaller then the sum of remaining sides