Question

The mean proportional between $6and24$ is

• A. $8$
• B. $12$
• C. $18$
• D. $24$

Answer 1

The correct option is B

$12$

Let the mean proportional be $x$, then

$6:x::x:24$

Now, if $a:b::c:d$are in proportion.

then, $a\times d=b\times c$ ---------------------------------$eq\left(1\right)$

So, here we have $6:x::x:24$

$a=6,b=x,c=x,d=24$

by using $eq\left(1\right)$ we have

$$\begin{gathered} \Rightarrow 6\times 24=x\times x \\ \Rightarrow x^2=144 \\ \Rightarrow x=\sqrt{144} \\ \Rightarrow x=12 \end{gathered}$$

Hence, the mean proportional between $6and24$ is $12$.

Therefore, OPTION (ii) is correct.