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

1 Answer
BeeFree
Jan 25, 2016

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

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