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Leelawati Virat Yohannan
Asked: 2022-11-02T17:45:42+05:30 In:

– If `log(5c/a),log((3b)/(5c))`and `log(a/(3b))`are in AP, where a, b, c are in GP, then a, b, c are the lengths ofsides of(A) an isosceles triangle(B) an equilateral triangle(D) none of these(C) a scalene triangle
A. an isosceles triangle
B. an equilateral triangle
C. a scalene triangle
D. none of these

– If `log(5c/a),log((3b)/(5c))`and `log(a/(3b))`are in AP, where a, b, c are in GP, then a, b, c are the lengths ofsides of(A) an isosceles triangle(B) an equilateral triangle(D) none of these(C) a scalene triangle
A. an isosceles triangle
B. an equilateral triangle
C. a scalene triangle
D. none of these
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  1. Correct Answer – D
    It is given that
    `log((5c)/(a)),log((3b)/(5c))andlog((a)/(3b))` are in A.P.,
    `rArr” “2log((3b)/(5c))=log((5c)/(a))+log((a)/(3b))`
    `rArr” “((3b)/(5c))^(2)=(5c)/(a)xx(a)/(3b)rArr3b=5c`
    Also, a,b,c are in G.P.
    `:.” “b^(2)=acrArr((5c)/(3))^(2)=acrArr25c^(2)=9acrArr25c=9a`
    `:.” “(9a)/(5)=5c=3b`
    `rArr” “(1)/(5//9)=(b)/(1//3)=(c)/(1//5)`
    `rArr” “(a)/(5)=(b)/(3)=(c)/(9//5)=lamda(“say”)rArra=5lamda,b=3lamdaandc=(9)/(5)lamda`
    We observe that `b+clta`.
    Thus, a,b,c cannot form the sides of a triangle.

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