Question

The mean proportional between 45 and a certain number is tree times the mean proportional between 45 and 22. The number is??

Answer 1

Let,

The mean proportional between 45 and a certain number be b and the unknown number be x

But,

mean  proportional (b)=square root of(a*c)

b=square root of(45*x)

b=square root of(9*5*x)

b=3*(square root of(5*x))

Also,

b is three times the mean proportional between 45 and 22

This means that,

b=3*(square root of(45*22))=3*3*(square root of(5*22))

3*(square root of(5*x))=3*3*(square root of(5*22))

3 and square root of(5) get cancelled

square root of(x)=3*(square root of(22))

Squaring on both sides

{square root of(x)}^2={(3)^2}*[{square root of(22)}^2]

x=9*22=198

Therefore the required number is 198