Question

Find two number whose mean proportion is $36$ and the third proportional is $288$.

Answer 1

Let the requird no be a and b

36 is the mean proportional between a and b

$\frac{a}{36}$ =$\frac{36}{b}$

ab=1296, a=$\frac{1296}{b}$

288 is the third proportion.

$\frac{a}{b}=\frac{b}{288}$

$b^2=a$

$b^2=288\times \frac{1296}{b}$

$b^3=373248$

b=72

$\therefore$ a= 18

$\therefore$ Two numbers are 18 and 72.