Question

the sides of a triangle are consecutive even integers .the perimeter of a triangle is 24 unit .what is the length of the shortest side.​

Answer 1

Answer:

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.

Step-by-step explanation:

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