Question

Find the sub-duplicate ratio of 9:16?

Answer 1

Hint: Here, first we will understand the meaning of the two types of ratio, namely duplicate and sub – duplicate ratio. Further, we will understand how to calculate the duplicate ratio and the sub – duplicate ratio of a given ratio a:b. Now, to find the sub – duplicate ratio of 9:16 we will take its square root and get the answer.

Complete step-by-step solution:
Here we have been provided with the ratio 9:16 and we are asked to calculate its sub – duplicate ratio. First we need to understand the meaning of the duplicate and the sub – duplicate ratio.
Now, in mathematics if we are provided with a ratio a:b and we are asked to find its duplicate ratio then what we do is we multiply the given ratio with itself after converting it into the fraction. So mathematically we have the duplicate ratio of a:b given as: -
$\Rightarrow \dfrac{a}{b}\times \dfrac{a}{b}=\dfrac{{{a}^{2}}}{{{b}^{2}}}$
Now, when we are asked to calculate the sub – duplicate ratio of a:b then what we do is we take the square root of the numerator and the denominator of the fractional form of the given ratio. So mathematically we have the sub – duplicate ratio of a:b given as:
$\Rightarrow \dfrac{\sqrt{a}}{\sqrt{b}}=\sqrt{\dfrac{a}{b}}$
Let us come to the question, we have to determine the sub – duplicate ratio of 9:16 so first converting it into the fraction we have $\dfrac{9}{16}$. Now, taking the square root of the numerator and the denominator we get,
$\Rightarrow \dfrac{\sqrt{9}}{\sqrt{16}}=\dfrac{3}{4}$
Hence, the sub – duplicate ratio of 9:16 is 3:4.

Note: You must remember the definitions of both the types of ratios to solve the above question as the terms may cause confusion. Do not consider the duplicate and the sub – duplicate ratio of a given ratio as its equivalent ratio because equivalent ratio is obtained when we multiply the numerator and the denominator of the fractional form of the ratio with the same constant other than 0.