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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

Jan 2, 2016

$2 \sqrt{3} i$ $2sqrt(3)i$
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:

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

$s = \frac{a + b + c}{2}$ $s = (a+b+c}/2$

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

Therefore $s = \frac{1 + 5 + 8}{2}$ $s = (1 + 5 + 8) / 2$
$s = 7$ $s = 7$

By Heron: $A = \sqrt{6.2 . - 1} = \sqrt{2.2 .3} i = 2 \sqrt{3} i$ $A = sqrt(6.2.-1) = sqrt(2.2.3 )i = 2sqrt(3)i$

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