a
The
area of
triangle is 84 cm. If
the length of the
sides
are
consecutive natural
number

1 thought on “a<br />The<br />area of<br />triangle is 84 cm. If<br />the length of the<br />sides<br />are<br />consecutive natural<br />number”

1. Answer:

   Let a=n−1,b=n,c=n+1;n∈N and n≥2

   ∴ larger angle =C and smallest angle =A

   Since the sides of triangle are in A.P., then C=2A

   sinC=sin2A⇒sinC=2sinAcosA

   ⇒2ac=cosA⇒2bcb2+c2−a2=2ac

   ⇒(n)(n+1)(n2)(n+1)2−(n−1)2=2(n−1)n+1

   ⇒n=5⇒a=4,b=5,c=6

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