Question

Find the value of $x$ if

$\left(ii\right)$ $(2x+1):(3x+13)$ is the sub-duplicate ratio of $9:25$

Answer 1

Step: Find the value of $x$

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

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

$=3:5$

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

$\Rightarrow 5(2x+1)=3(3x+13)\left[\text{cross product}\right]$

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

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

$\Rightarrow x=34$

Hence, the value of $x\text{is}34.$