Question

Find the fourth proportional to
48, 12, 64

Answer 1

Hint: In this question let the fourth proportional to be a variable. Use the concept that if four numbers a, b, c and d are to be in proportion that $\dfrac{a}{b} = \dfrac{c}{d}$, to get the value of this unknown.

Complete step-by-step answer:
Given numbers are

48, 12, 64

Now we have to find out the fourth proportionality.

Let the fourth proportional be x.

Now according to the proportional theorem the ratio of first and second number should be equal to third and fourth.

$ \Rightarrow 48:12::64:x$

This ratio is also written as

$ \Rightarrow \dfrac{{48}}{{12}} = \dfrac{{64}}{x}$

Now simplify the above equation we have,

$ \Rightarrow \left( {48 \times x} \right) = \left( {64 \times 12} \right)$

Now divide by 48 throughout we have,

$ \Rightarrow x = \left( {\dfrac{{64 \times 12}}{{48}}} \right) = \dfrac{{64}}{4} = 16$

So the fourth proportional is 16.

So this is the required answer.

Note: A proportion is simply a statement that two ratios are equal. It comes under the category of ratios and proportions. There are in general four proportions used in mathematics namely as Direct proportion, Inverse proportion, Compound proportion and Continued proportion.