Third Proportion Calculation

To find the third proportion (let's call it '$c$') to two numbers '$a$' and '$b$', we use the concept of continued proportion. If '$a$', '$b$', and '$c$' are in continued proportion, the ratio between the first two numbers is equal to the ratio between the second and the third number.

This can be written as:

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

Applying the Formula

In this problem, we are given the numbers $a = 12$ and $b = 30$. We need to find the third proportion, '$c$'.

Set up the proportion:

$ \frac{12}{30} = \frac{30}{c} $

Solving for the Third Proportion

To find '$c$', we can cross-multiply:

$ 12 \times c = 30 \times 30 $

Calculate the product on the right side:

$ 12c = 900 $

Now, isolate '$c$' by dividing both sides by 12:

$ c = \frac{900}{12} $

Perform the division:

$ c = 75 $

Therefore, the third proportion to 12 and 30 is 75.