Solving the Equation for X

The problem asks us to find the positive value of the variable X that satisfies the given equation:

$$ \frac{X}{147} = \frac{48}{X} $$

This is an algebraic equation involving fractions. To solve for X, we can use the method of cross-multiplication.

Step-by-Step Solution

1. Cross-Multiplication: Multiply the numerator of the left fraction by the denominator of the right fraction, and set it equal to the product of the denominator of the left fraction and the numerator of the right fraction.

   $$ X \times X = 147 \times 48 $$ $$ X^2 = 147 \times 48 $$

2. Calculate the Product: Now, we need to calculate the value of $147 \times 48$.

   Let's perform the multiplication:

   $$ 147 \times 48 = 7056 $$

   So the equation becomes:

   $$ X^2 = 7056 $$

3. Find the Square Root: To find the value of X, we need to take the square root of both sides of the equation.

   $$ X = \pm \sqrt{7056} $$

   The question specifically asks for the positive value of X.

4. Calculate the Square Root of 7056: We need to find a number that, when multiplied by itself, equals 7056.

   We can estimate or use calculation methods. Let's test values. We know $80^2 = 6400$ and $90^2 = 8100$. Since 7056 ends in 6, its square root must end in 4 or 6.

   Let's try 84:

   	84
   x	84
   ----	----
   	336 (84 * 4)
   	6720 (84 * 80)
   ----	----
   	7056

   
   

   So, $\sqrt{7056} = 84$.

5. Determine the Positive Value: Since $X^2 = 7056$, the possible values for X are $X = 84$ and $X = -84$. As the question asks for the positive value, we choose 84.

   $$ X = 84 $$

Therefore, the positive value of X that satisfies the equation is 84.