Question

A triangle has sides with lengths: 6, 1, and 5. How do you find the area of the triangle using Heron's formula?

Answer 1

First, find the semiperimeter `s=(1/2)(6+1+5)=6`. Now, use Heron's area formula ...

Explanation:

Heron's Area `=sqrt(s(s-a)(s-b)(s-c))`

Area `=sqrt(6(6-6)(6-1)(6-5))=0`

Why is the area 0?

The Triangle Inequality Theorem states that the length of any side of a triangle MUST be less than the sum of the other two sides. For this problem, the theorem fails the test :

`6` is not less than `1+5`

So, a triangle with sides 6, 1 and 5 is not a triangle!

hope that helped