Finding the Third Proportional

The question asks for the third proportional to the numbers 16 and 36.

Understanding Third Proportional

If three numbers $a$, $b$, and $c$ are in continued proportion, it means the ratio of the first two numbers is equal to the ratio of the second and third numbers.

Mathematically, this is represented as:

$ a : b :: b : c $

This can also be written as a fraction:

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

In this problem, we have $a = 16$ and $b = 36$. We need to find the third proportional, $c$.

Calculating the Third Proportional

To find $c$, we can rearrange the proportion formula:

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

Substitute the given values ($a = 16$, $b = 36$):

$ c = \frac{36 \times 36}{16} $

Calculate the value:

1. First, calculate $36 \times 36$: $ 36 \times 36 = 1296 $
2. Now, divide the result by 16: $ c = \frac{1296}{16} $ $ c = 81 $

Therefore, the third proportional to 16 and 36 is 81.