Question

A right triangle has hypotenuse 8 and area 8. Find the perimeter?

I think I have to use Heron's Formula for this question. Please help & show work. Thank you very much. Your work is very much appreciated.

Answer 1

h^2=a^2+b^2
64=a^2+b^2
but 1/2 ab=8 so a= 16/b

then
64=(16/b)^2 + b^2
64b^2=256+b^4
let u= b^2
64u=256+u^2
u^2-64u+256=0

u= 1/2 (64+-sqrt(64^2-4*256)
U=4.28718708, 59.71
so a= sqrt u= 7.73, or= 2.07
then b= 2.06, or 7.73

Perimeter: 8 + 7.73+2.06