Question

Find the third proportion to $4.5,6$

Answer 1

The third proportion of two numbers a and b is defined to be that number c such that $a:b::b:c$

Let the third proportion be $x$

Therefore third proportion of $4.5,6$ will be given as

$4.5:6::6:x$

$\Rightarrow \frac{4.5}{6}=\frac{6}{x}$

Cross multiply

$\Rightarrow 4.5\times x=6\times 6$

$\Rightarrow 4.5\times x=36$

$\Rightarrow x=\frac{36}{4.5}$

On calculating

$\Rightarrow x=8$