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- 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 triangleA. an isosceles triangleB. an equilateral triangleC. a scalene triangleD. none of these |
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Answer» 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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