If `root(2)(0.014xx0.14x)=0.014xx0.14root(2)y` then `x/y` is equal to

Options

A. a)0.000196
B. b)0.00196
C. c)0.0196
D. d)0.196

Answer

To solve the equation \( \sqrt{2}(0.014 \times 0.14x) = 0.014 \times 0.14\sqrt{2}y \), we will follow these steps:

### Step 1: Simplify the equation
We can start by simplifying both sides of the equation. The left-hand side is:
\[ \sqrt{2} \times (0.014 \times 0.14x) = 0.014 \times 0.14 \times \sqrt{2} \times x \]
The right-hand side is:
\[ 0.014 \times 0.14 \times \sqrt{2} \times y \]
Thus, we can rewrite the equation as:
\[ 0.014 \times 0.14 \times \sqrt{2} \times x = 0.014 \times 0.14 \times \sqrt{2} \times y \]

### Step 2: Cancel common terms
Since \(0.014 \times 0.14 \times \sqrt{2}\) is common on both sides, we can cancel it out (assuming it is not zero):
\[ x = y \]

### Step 3: Find the ratio \( \frac{x}{y} \)
From the equation \(x = y\), we can express the ratio:
\[ \frac{x}{y} = \frac{y}{y} = 1 \]

### Conclusion
Thus, the value of \( \frac{x}{y} \) is:
\[ \frac{x}{y} = 1 \]