Question

Find the third proportion to $12,16$

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 $12,16$ will be given as

$12:16::16:x$

$\Rightarrow \frac{12}{16}=\frac{16}{x}$

Cross multiply

$\Rightarrow 12\times x=16\times 16$

$\Rightarrow 12\times x=256$

$\Rightarrow x=\frac{256}{12}$

On simplifying

$\Rightarrow x=\frac{64}{3}$