Question

if a,b,,c are the length of the sides of a triangle such that,(i) a,b,c are in G.P. and (ii) log a-log b,log2b-log3c and log3a-loga are in AP,then the triangle is (a) equilateral (b) acute angled (c) obtuse angled (d) right angled
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Answer 1

Answer:

obtuse angle

Step-by-step explanation:

As given, b2=ac and

2(log2b−log3c)=loga−log2b+log3c−loga

⇒b2=ac and 2b=3c

⇒b=32a and c=94a

Since, a+b=35a>c, b+c=910a>a, c+a=913a>b

It implies that a,b,c form a triangle with a as the greatest side.

Now, for finding greatest ∠A of ΔABC, we use cosine formula

cosA=2bcb2+c2−a2=−4829<0

∴ The angle A is obtuse. Hence, a,b,c are the lengths of sides of an obtuse angled triangle.