Find the mean proportional between $16 a n d 9$

Open in App

Solution

A continued proportional of three quantities $a, b a n d c$ is written as $a : b : : b : c$
where, $a i s f i r s t p r o p o r t i o n a l,$ $b i s t h e m e a n p r o p r t i o n a l$ and $c i s t h i r d p r o p o r t i o n a l$
Step-1: Write $a a n d b$ as it should be in the form of $a : b : : b : c$ for third proportional
$a = 6$ $c = 12$
Step-2: Write mean terms and extreme terms
$m e a n t e r m : -$ $b$
$e x t r e m e t e r m : -$ $a = 16$ and $c = 9$
Step-3: Find $m e a n p r o p r t i o n a l$
As $p r o d u c t o f m e a n s = p r o d u c t o f e x t r e m e s$
$b \times b = a \times c b^{2} = 16 \times 9 b^{2} = 144 b = \sqrt{144} b = 12$
Hence, the $m e a n p r o p r t i o n a l$ is $b = 12$

Suggest Corrections

Similar questions

The mean proportional between $9$ and $16$ is
$(a) 12.5$
$(b) 12$
$(c) 5$
$(d)$ none of these

Solve the following.

Find the mean proportion between 9 and 49.

16

4

Join BYJU'S Learning Program