Question

if(2x3):(5x+4) is the triplicate ratio of 3:4, find the square of x.

Answer 1

Answer: 144

Step-by-step explanation:

Since the triplicate ratio of $\frac{3}{4}$ = $\frac{3^3}{4^3} = \frac{27}{64}$

But, According to the question,

$\frac{2x+3}{5x+4}$  is the triplicate ratio of $\frac{3}{4}$,

⇒ $\frac{2x+3}{5x+4} = \frac{27}{64}$

⇒ $64(2x+3) = 27(5x+4)$

⇒ $128x+192 = 135x+108$

⇒ $128x-135x=108-192$

⇒ $-7x=-84$

⇒ $x = 12$

Thus, the square of x = $(12)^2 = 144$

⇒ Option C is correct.

Answer 2

Answer:

$\Rightarrow x^2=144$

Step-by-step explanation:

We have been given that the

$\frac{2x+3}{5x+4}$ is triplicate ratio of 3:4

And actually the triplicate ratio of

$3:4=3^3:4^3$

$\Rightarrow 27:64$

On equating the actual and given condition we get:

$\frac{2x+3}{5x+4}=\frac{27}{64}$

$\Rightarrow 64(2x+3)=27(5x+4)$

$\Rightarrow 128x+192=135x+108$

$\Rightarrow 135x-128x=192-108$

$\Rightarrow 7x=84$

$\Rightarrow x=12$

And then $x^2=12^2$

$\Rightarrow x^2=144$