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What should come in place of both x in the equation $$\frac{x}{{\sqrt {128} }} = \frac{{\sqrt {162} }}{x}$$

A. 12

B. 14

C. 144

D. 196

Answer: Option A

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let}}\,\frac{x}{{\sqrt {128} }} = \frac{{\sqrt {162} }}{x} \cr & {\text{Then}}\,{x^2} = \sqrt {128 \times 162} \cr & = \sqrt {64 \times 2 \times 18 \times 9} \cr & = \sqrt {{8^2} \times {6^2} \times {3^2}} \cr & = 8 \times 6 \times 3 \cr & = 144 \cr & \therefore x = \sqrt {144} = 12 \cr} $$

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