Question

Find the third proportional to 1.2, 0.6.

Answer 1

Hint: Here, by the definition we can say that the third proportional of two numbers a and b is defined to be that number c such that a : b = b : c . Therefore we can write 1.2, 0.6 in the form:
$\dfrac{1.2}{0.6}=\dfrac{0.6}{x}$ where $x$ is the third proportional. Next find the value of $x$.

 Complete step-by-step solution -
Here, we are given with two numbers 1.2, 0.6.
Next, we have to find the third proportional.
Hence, we can say that, if two ratios a : b and c : d are in proportion if $\dfrac{a}{b}=\dfrac{c}{d}$ and we write,
 a : b : : c : d
Also, we have if a, b and c are in continued proportion then c is called the third proportional.
 We know that the third proportional of two numbers a and b is defined to be that number c such that a: b : : b : c that is, $\dfrac{a}{b}=\dfrac{b}{c}$. Hence the third proportional of a proportion is the second term of the mean terms.
Now, let the third proportional be $x$.
 Then by the definition of third proportional we can write:
$\dfrac{1.2}{0.6}=\dfrac{0.6}{x}$
Next, by cancellation we get:
$2=\dfrac{0.6}{x}$
Now, by cross multiplication we obtain:
$x=\dfrac{0.6}{2}$
Then, by cancellation we will get the value of $x$.
$\Rightarrow x=0.3$
 Therefore we can write in the form:
$\dfrac{1.2}{0.6}=\dfrac{0.6}{0.3}$
That is, 1.2: 0.6 = 0.6 : 0.3
Hence, the third proportional to 1.2, 0.6 is 0.3.

Note: Here, you should be aware that the third proportional is the second term of the mean terms.
If $\dfrac{1.2}{0.6}=\dfrac{0.6}{x}$, don’t write $x=0.6$. Here, you have to do the cross multiplication to get the value of $x$.