Question

How do you find the third proportion of 6 and 12?

Answer 1

Hint: The third proportional of two integers a and b is defined as the number c such that $a:b = b:c$ according to the definition. As a result, 6 and 12 may be written as $6:12 = 12:c$, where c is the third proportional. Next, we will determine c's value.

Complete step by step solution:
We have two numbers presented to us: 6 and 12.
We have to find the third proportionate.
We know that if two ratios $a:b$ and $c:d$ are in proportion if $ \Rightarrow c = 24$$\dfrac{a}{b} = \dfrac{c}{d}$
We can write it as $a:b::c:d$
Also, if a, b, and c are in constant proportion, c is referred to as the third proportional.
We know that the third proportional of two integers a and b is defined as the number c such that $a:b = b:c$ that is $\dfrac{a}{b} = \dfrac{b}{c}$ .
As a result, the second term of the mean terms is the third proportional of a percentage.
We assume c to be the third proportionate.
So, by definition
$ \Rightarrow \dfrac{a}{b} = \dfrac{b}{c}$
We will substitute a equals to 6 and b equals to 12
$ \Rightarrow \dfrac{6}{{12}} = \dfrac{{12}}{c}$
We cross multiply
$ \Rightarrow 6c = 144$
Then divide the equation by 6
$ \Rightarrow c = 24$
Hence, the third proportional of 6 and 12 is 24.

Note:
 It's worth noting that in both ratios, the middle number should be the common word, while the first term should be the rare term, therefore $\dfrac{a}{b} = \dfrac{b}{c}$ must be used in any percentage computations.