Find the value of $x$ if

$(i i)$ $(2 x + 1) : (3 x + 13)$ is the sub-duplicate ratio of $9 : 25$

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Solution

Step: Find the value of $x$

Square root of given ratio is the sub-duplicate ratio.

$∴$ Sub-duplicate ratio of $9 : 25 = \sqrt{9} : \sqrt{25}$

$= 3 : 5$

Now, $\frac{2 x + 1}{3 x + 13} = \frac{3}{5}$

$\Rightarrow 5 (2 x + 1) = 3 (3 x + 13) [cross product]$

$\Rightarrow 10 x + 5 = 9 x + 39$

$\Rightarrow 10 x - 9 x = 39 - 5$

$\Rightarrow x = 34$

Hence, the value of $x is 34.$

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