Home/ Questions/Q 469093
Next
In Process
Tanay Prasad Barad
Asked: 2022-11-11T17:41:27+05:30 In:

If the sides of a triangle are in G.P., and its largest angle is twicethe smallest, then the common ratio `r`satisfies the inequality`0A. `0ltrltsqrt(2)`
B. `1ltrltsqrt(2)`
C. `1ltrlt2`
D. none of these

If the sides of a triangle are in G.P., and its largest angle is twicethe smallest, then the common ratio `r`satisfies the inequality`0A. `0ltrltsqrt(2)`
B. `1ltrltsqrt(2)`
C. `1ltrlt2`
D. none of these
Parabola
Leave an answer

Leave an answer

Browse

1 Answer

  1. Correct Answer – B
    Let the sides of the triangle be `a//r`, a and ar, with `agt0gtandrgt1`.
    Let `alpha` be the smallest angle, so that the largest angle is `2alpha`. Then, `alpha` is opposite to the side `a//r and2alpha` is opposite to the side ar. Applying sine rule, we get
    `(a//r)/(sinalpha)=(ar)/(sin2alpha)`
    `rArr” “(sin2alpha)/(sinalpha)=r^(2)`
    `rArr2cosalpha=r^(2)`
    `rArr” “r^(2)lt2” “[becausealpha!=:.2cosalphalt2]`
    `rArr” “rltsqrt(2)`
    Hence, `1ltrltsqrt(2)`

    • 0