In a triangle ABC, a = 2b and `angle A = 3 angle B`. Which one of the following is correct ?

Options

A. The triangle is isosceles
B. The triangle is equilateral
C. The triangle is right-angled
D. Such triangle does not exist

Answer

C

Explanation

From properties of triangle we know that
`(a)/(sin A)=(b)/(sin B)=(c)/(sin C)`
Given that a = 2b and A = 3B.
We get `(2b)/(sin 3B)=(b)/(sin B)`.
`rArr (sin 3B)/(sin B)=2 rArr (3sin B - 4 sin^(3)B)/(sin B)=2`
`rArr 3 - 4 sin^(2) B = 2`
`rArr sin^(2)B=((1)/(2))^(2)rArr sinB = (1)/(2)= "sin"(pi)/(6)`
`rArr B = (pi)/(6)"since"A = 3 B`
So, `angle A = (pi)/(2)`
Thus, triangle is right angled triangle.