How do you use Heron's formula to find the area of a triangle with sides of lengths $3$ , $5$ , and $5$ ?

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Answer 1 · 2016-01-27T13:07:03

$"Area"_triangle=7/4sqrt(39)$

Given sides $(a,b,c) = (3,3,5)$
the semi-perimeter is $s=(3+3+5)/2 = 13/2$

and by Heron's formula: $"Area"_triangle = sqrt(s(s-a)(s-b)(s-c))$

So
$color(white)("XXX")"Area"_triangle = sqrt(13/2xx7/2xx7/2xx3/2)$

$color(white)("XXXXXXX")=sqrt((13xx3xx7^2)/(4^2))$

$color(white)("XXXXXX")=7/4sqrt(39)$

How do you use Heron's formula to find the area of a triangle with sides of lengths 3 3 , 5 5 , and 5 5 ?