Question

Find the third proportion to: 21÷4 and 7​

Answer 1

$\huge \bold{ANSWER}$

First we need to know what is proportion?

▶Four non zero quantities a, b, c and d are said to be in proportion (or, are proportional), if a : b = c : d.

This is often expressed as a : b :: c : d

In which

▶a : b = c : d

i) a, b, c and are called the terms of proportionate; where a = first term, b = second term, c = third term and d = fourth term.

ii) a and d are called extremes whereas c and d are called means.

▶a : b = c : d

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

a × d = b × c

✳product of means = product of extremes.

▶In a : b = c : d, the fourth term d is the fourth proportional.

SO, IN QUESTIONS 21,4 and 7 to find fourth proportional as d,

▶$\frac{a}{b} = \frac{c}{d}$

▶$\frac{21}{7} = \frac{4}{d}$

On cross multiplication,

▶$\frac{21}{7\times4} = d$

▶$\frac{3}{4} = d$