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The sides of A B C satisfy the equation...

The sides of ` A B C` satisfy the equation `2a^2+4b^2+c^2=4a b+2ac` Then a) the triangle is isosceles b) the triangle is obtuse c) `B=cos^(-1)(7/8)` d) `A=cos^(-1)(1/4)`

A

the triangle is isosceles

B

the triangle is obtuse

C

`B = cos^(-1) (7//8)`

D

`A = cos^(-1) (1//4)`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`(a^(2) - 2ac + c^(2)) + (a^(2) - 4ab+ 4b^(2)) = 0`
or `(a-c)^(2) + (a-2b)^(2) = 0`
`rArr a = c and a = 2b`
Therefore, the triangle is isosceles.
Also, `cos B = (a^(2) + c^(2) -b^(2))/(2ac) = (7b^(2))/(8b^(2)) = (7)/(8)`
`cosA = (b^(2) + c^(2) -a^(2))/(2bc) = (1)/(4)`
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Knowledge Check

  • The sides of a triangleABC satisfy the equation 2a^(2) + 4b^(2) + c^(2) =4ab + 2ac , then-

    A
    the triangle is isoceles
    B
    the triangle is obtuse
    C
    `B= cos^(-1) 7/8`
    D
    `A = cos^(-1) 1/4`

  • In triangle ABC, If cos B= a/(2c) , then the triangle is-

    A
    equilateral
    B
    isosceles
    C
    right angled
    D
    scalene.

  • In a triangle ABC if there angles are A,B,C then cos ((A+B)/2)

    A
    cos C/2
    B
    (-sinC)
    C
    sin C/2
    D
    cos C

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