If `(37)/(4 sqrt(j)-19)=(37)/(17)`, then j =

Options

A. 64
B. `72.25`
C. 81
D. `90.25`

Explanation

To solve the equation \(\frac{37}{4 \sqrt{j} - 19} = \frac{37}{17}\), we can follow these steps:

### Step 1: Cross-Multiply
We start by cross-multiplying to eliminate the fractions:
\[ 37 \cdot 17 = 37 \cdot (4 \sqrt{j} - 19) \]

### Step 2: Simplify the Equation
Since \(37\) is common on both sides, we can cancel it out (assuming \(37 \neq 0\)):
\[ 17 = 4 \sqrt{j} - 19 \]

### Step 3: Isolate the Term with \(\sqrt{j}\)
Next, we add \(19\) to both sides to isolate the term with \(\sqrt{j}\):
\[ 17 + 19 = 4 \sqrt{j} \]
\[ 36 = 4 \sqrt{j} \]

### Step 4: Solve for \(\sqrt{j}\)
Now, we divide both sides by \(4\) to solve for \(\sqrt{j}\):
\[ \sqrt{j} = \frac{36}{4} \]
\[ \sqrt{j} = 9 \]

### Step 5: Square Both Sides
To find \(j\), we square both sides:
\[ j = 9^2 \]
\[ j = 81 \]

### Final Answer
Thus, the value of \(j\) is:
\[ \boxed{81} \]

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