Find the value of $$x$$ if $$\frac{x}{\sqrt{128}} = \frac{\sqrt{162}}{x}$$​

Correct option is D

Given: 

​$$\frac{x}{\sqrt{128}} = \frac{\sqrt{162}}{x}$$ 

Solution:

Multiply both sides of the equation by $$x \cdot \sqrt{128}$$ to eliminate the fractions:

​$$x^2 = \sqrt{128} \cdot \sqrt{162}$$ 

Simplify the Square Roots: 

​$$\sqrt{128}$$ = $$\sqrt{64 \cdot 2} = \sqrt{64} \cdot \sqrt{2} = 8\sqrt{2}$$ 

​$$\sqrt{162} = \sqrt{81 \cdot 2} = \sqrt{81} \cdot \sqrt{2} = 9\sqrt{2}$$ 

Now, 

​$$x^2 = (8\sqrt{2}) \cdot (9\sqrt{2})$$ 

​$$x^2 = 8 \cdot 9 \cdot \sqrt{2} \cdot \sqrt{2}$$ 

​$$x^2 = 8 \cdot 9 \cdot 2 = 144$$ 

​$$x = \sqrt{144} = 12$$ 

The value of x is 12