Question

Find out
(i) the fourth proportional to 4, 9, 12
(ii) the third proportional to 16 and 36
(iii) the mean proportional between 0.08 and 0.18

• A. $27,81,0.12$
• B. $27,81,1.2$
• C. $9,27,0.12$
• D. $27,9,0.12$

Answer 1

The correct option is A $27,81,0.12$

(i) Let the fourth proportional to $4,9,12$ be $x$

Then $4:9::12:x$
$\Rightarrow 4\times x=9\times 12$

$\Rightarrow x=\frac{9\times 12}{4}=27$
Therefore, fourth proportional to $4,9,12$ is $27$.
(ii) Let the third proportional to $16$ and $36$ is $x$

Then $16:36::36:x$

$\Rightarrow$ $16\times X=36\times 36$
$\Rightarrow x=\frac{36\times 36}{16}=81$
Therefore, third proportional to $16$ and $36$ is $81$.
(iii) Mean proportional between $0.08$ and $0.18$
$=\sqrt{0.08\times 0.18}=\sqrt{\frac{8}{100}\times \frac{18}{100}}$
$=\sqrt{\frac{144}{100\times 100}}=\frac{12}{100}=0.12$