Question

Find the third proportion of 1.8 and 0.6.

Answer 1

Hint: In this question, we need to determine the third proportion of 1.8 and 0.6. For this, we will follow the relation between the proportions and evaluate the result.

Complete step-by-step answer:
The third proportional is the variable in a continued proportion with two equal terms. A third proportional is equal to the square of the equal terms, divided by the unequal term. Mathematically, $ \dfrac{a}{b} = \dfrac{b}{c} $ where ‘c’ is the third proportion for the numbers ‘a’ and ‘b’.
In other words, $ c = \dfrac{{{b^2}}}{a} $ where, ‘b’ is the common term and ‘a’ is the unequal term.
Now, according to the question, we need to determine the third proportion for the numbers 1.8 and 0.6. So, comparing it with the standard third proportion formula a=1.8 and b=0.6.
Substituting the values of ‘a’ and ‘b’ in the equation $ \dfrac{a}{b} = \dfrac{b}{c} $ to determine the value of the third proportion.
 $
  \dfrac{a}{b} = \dfrac{b}{c} \\
  \dfrac{{1.8}}{{0.6}} = \dfrac{{0.6}}{c} \\
  $
Cross-multiplying the terms of the above equation, we get
 $
  \dfrac{{1.8}}{{0.6}} = \dfrac{{0.6}}{c} \\
   \Rightarrow 1.8c = 0.6 \times 0.6 \\
   \Rightarrow 1.8c = 0.36 \\
  $
Now, bringing 1.8 from the left hand side of the above equation to the right hand side, we get
\[
\Rightarrow 1.8c = 0.36 \\
\Rightarrow c = \dfrac{{0.36}}{{1.8}} \\
   = \dfrac{{36}}{{18}} \times \dfrac{{10}}{{100}} \\
   = \dfrac{2}{{10}} \\
   = 0.2 \\
 \]
Hence, the third proportion for the numbers 1.8 and 0.6 is equals to 0.2.

Note: It must be noted here that the middle number should be the common term in both the ratios while the first term is the uncommon term such that $ \dfrac{a}{b} = \dfrac{b}{c} $ must be followed in any proportion calculations.