Question

Ina triangle abc a,b,a are given and c1,c2 are two values of the third side
c.The sum of the areas of two triangles with sides a,b,c1 and a,b,c2 is

Answer 1

Answer:

From cosine rule we have

⇒c

2

−2bccosA+b

2

−a

2

=0

let c

1

and c

2

be the roots of the above equation.

The sum of the roots = c

1

+c

2

=2bcosA

Now, sum of area of two triangle=Δ=Δ

1

+Δ

2

=

2

bc

1

sinA+bc

2

sinA

=

2

b(c

1

+c

2

)sinA

⇒△=b

2

cosAsinA=

2

b

2

sin2A