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

Question

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

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Adalynn 3 months 2021-07-17T13:19:35+00:00 1 Answers 0 views 0

Answers ( )

    0
    2021-07-17T13:21:16+00:00

    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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