If a : b = b : c, then a : c is equal to : 1. b : a 2. b2 : a2 3. a2 : b2 4. b : c

Given, ⇒ a : b = b : c ⇒ ⇒ b2 = ac ⇒ c = Substituting values in a : c, we get : Hence, Option 3 is the correct option.

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Mathematics

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Given,

⇒ a : b = b : c

⇒ $\dfrac{a}{b} = \dfrac{b}{c}$

⇒ b² = ac

⇒ c = $\dfrac{b^2}{a}$

Substituting values in a : c, we get :

$\Rightarrow a : c = a : \dfrac{b^2}{a} \\[1em] = \dfrac{a}{\dfrac{b^2}{a}} \\[1em] = \dfrac{a^2}{b^2} \\[1em] = a^2 : b^2.$

Hence, Option 3 is the correct option.

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