##
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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Mathematics
3 months
2021-07-17T13:19:35+00:00
2021-07-17T13:19:35+00:00 1 Answers
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## Answers ( )

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