Question

The area of a triangle is 84 cm2. If the length of the sides are consecutive natural numbers, then what are the dimensions (in cm) of the triangle?​

Answer 1

Answer:

Correct option is

B

4,5,6

Using sine law,

n−1

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.