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)

1 thought on “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)”

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.

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