Question

Let l, m, n be three consecutive natural numbers (l> m>n). If the angle A of ∆ABC be given by sin A = (a² + b² + c² )(l² + m² + n²)/(al+bm+cn)² and the perimeter of the triangle is 12 unit, then the area of the '∆ABC is .
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Answer 1

Answer:

Le, n be three consecutive natural numbers (l> m>n). If the angle A of ∆ABC be given by sin A = (a² + b² + c² )(l² + m² + n²)/(al+bm+cn)² and the perimeter of the triangle is 12 unit, then the area of the

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Correct option is B)

Using sine law,

n−1 =

sinα n+1

sin2α

sinα

=

n+1

sin2α

⇒2cosα=

(n−1)

n+1

⇒cosα=

2(n−1)

n+1

∴

2n(n+1)

n

2

+(n+1)

2

−(n−1)

2

=

2(n−1)

(n+1)

(using cosine law)

⇒

2n+(n+1)

n

2

+4n

=

2(n−1)

(n+1)

⇒

2(n+1)

n+4

=

2(n−1)

n+1

⇒(n+1)

2

=(n+4)(n−1)

∴n=5

Hence, lengths of the side of the triangle are 4,5 and 6.