Question

A triangle has sides with lengths: 1, 5, and 8. How do you find the area of the triangle using Heron's formula?

Answer 1

`2sqrt(3)i`
This is an unsatisfactory result as it demonstrates that this triangle cannot exist.

Explanation:

Heron's formula states that the area of a triangle whose sides have lengths a, b, and c is:

`A=sqrt {s(s-a)(s-b)(s-c)}`
where s is the semiperimeter of the triangle; that is,

`s = (a+b+c}/2`

In this case; a = 1, b = 5, c = 8

Therefore `s = (1 + 5 + 8) / 2`
`s = 7`

By Heron: `A = sqrt(6.2.-1) = sqrt(2.2.3 )i = 2sqrt(3)i`