Question

A triangle has sides with lengths: 4, 12, and 2. How do you find the area of the triangle using Heron's formula?

Answer 1

No such triangle is possible since no triangle can have a side which is longer than the sum of the other two sides (at least in Euclidean space)

Explanation:

If you attempted to apply Heron's formula:
`color(white)("XXX")Area = sqrt(s(s-a)(s-b)(s-c))`
for a triangle with sides `a=4, b=12, c=2`
and semi-perimeter `s=9` (i.e. `(a+b+c)/2`)

you would end up attempting to find the square root of a negative number: `sqrt(9 * (5) * (-3) * (7))`