Question

Show that the following numbers are in continued proportion:

(i) 36, 90, 225
(ii) 48, 60, 75
(iii) 16, 84, 441

Answer 1

(i) 36, 90, 225

Consider $\frac{36}{90}=\frac{2}{5}$ (Dividing numerator and denominator by 18)

$\frac{90}{225}=\frac{2}{5}(\mathrm{Dividing}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\mathrm{by}45)$

$\Rightarrow$ 36 : 90 : : 90 : 225

(ii) 48, 60, 75

Consider $\frac{48}{60}=\frac{4}{5}$ (Dividing numerator and denominator by 12)

$\frac{60}{75}=\frac{4}{5}(\mathrm{Dividing}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\mathrm{by}15)$

$\Rightarrow$ 48 : 60 : : 60 : 75

(iii) 16, 84, 441

Consider $\frac{16}{84}=\frac{4}{21}$ (Dividing numerator and denominator by 4)

$\frac{84}{441}=\frac{4}{21}(\mathrm{Dividing}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\mathrm{by}21)$

$\Rightarrow$16 : 84 : : 84 : 441