Home
Class 12
MATHS
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)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Linked comprehension type|34 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Matrix match type|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Exercises|80 Videos

  • PROGRESSION AND SERIES

    CENGAGE ENGLISH|Exercise ARCHIVES (MATRIX MATCH TYPE )|1 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise Archives(Matrix Match Type)|1 Videos

Similar Questions

Explore conceptually related problems

The sides of triangle ABC satisfy the relations a + b - c= 2 and 2ab -c^(2) =4 , then the square of the area of triangle is ______

If the sines of the angles A and B of a triangle ABC satisfy the equation c^2x^2-c(a+b)x+a b=0 , then the triangle (a) is acute angled (b) is right angled (c) is obtuse angled (d) satisfies the equation sinA+cosA ((a+b))/c

Knowledge Check

  • In triangle ABC, a = 2, b = 3,c = 4 , then the value of cos A is

    A
    `21/24`
    B
    `21/12`
    C
    `24/21`
    D
    `24/12`

    • Similar Questions

    Explore conceptually related problems

    If in a Delta A B C ,cos^2A+cos^2B+cos^2C=1, prove that the triangle is right angled.

    If in Delta ABC, c(a+b) cos ""B/2=b (a+c) cos ""C/2, the triangle is

    In a triangle A B C , if cos A=(sinB)/(2sinC) , show that the triangle is isosceles.

    If sinA=sin^2Ba n d2cos^2A=3cos^2B then the triangle A B C is right angled (b) obtuse angled (c)isosceles (d) equilateral

    If one of the angles A,B,C of a triangle is not acute, show that cos^2A+cos^2B+cos^2C=1

    If in a triangle ABC, (bc)/(2 cos A) = b^(2) + c^(2) - 2bc cos A then prove that the triangle must be isosceles.

    If in a triangle a cos^2C/2+cos^2A/2=(3b)/2, then find the relation between the sides of the triangle.

    Home
    Profile