Question

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

Answer 1

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

Explanation:

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)`