If `sqrt(1+(x)/(144))=(13)/(12)`, then x equals to

Options

A. 1
B. 13
C. 27
D. 25

Answer

To solve the equation \( \sqrt{1 + \frac{x}{144}} = \frac{13}{12} \), we will follow these steps:

### Step 1: Square both sides
To eliminate the square root, we square both sides of the equation.

\[ \left(\sqrt{1 + \frac{x}{144}}\right)^2 = \left(\frac{13}{12}\right)^2 \]

This simplifies to:

\[ 1 + \frac{x}{144} = \frac{169}{144} \]

### Step 2: Isolate the term with x
Next, we want to isolate the term containing \( x \). We do this by subtracting 1 from both sides.

\[ \frac{x}{144} = \frac{169}{144} - 1 \]

To subtract 1, we can express 1 as \( \frac{144}{144} \):

\[ \frac{x}{144} = \frac{169}{144} - \frac{144}{144} \]

This simplifies to:

\[ \frac{x}{144} = \frac{169 - 144}{144} = \frac{25}{144} \]

### Step 3: Solve for x
Now, we multiply both sides by 144 to solve for \( x \):

\[ x = 144 \cdot \frac{25}{144} \]

This simplifies to:

\[ x = 25 \]

### Final Answer
Thus, the value of \( x \) is \( 25 \).

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