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

1 Answer
Alan N.
Jan 2, 2016

#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#

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