The sides of the triangle are ( y/z + z/x ) , ( z /x + x / y ) and ( x /y + y / z ) then its area is
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Answer:
Step-by-step explanation:
The given sides of a triangle are;
a = y/z+z/x
b = z/x+x/y
c = x/y+y/z
We can find the area of the triangle by using Heron's formula;
Area = Sqr (s x (s-a) x (s-b) x (s-c))
where a, b, c are the sides of the triangle and s = (a + b c)/2
s = (a + b c)/2
= (y/z + z/x + z/x + x/y + x/y + y/z)/2
= 2 x (x/y + y/z + z/x) / 2
= x/y + y/z + z/x
Area = Sqr (s x (s-a) x (s-b) x (s-c))
= Sqr ((x/y + y/z + z/x) x (x/y) x (y/z) x (z/x))
= Sqr (/ + xy/yz + xz/xy + xy/yz + / + yz/xz + xz/xy + yz/xz + /)
= Sqr [/ + / + / + 2(xy/yz + xz/xy + yz/xz)]