What is the fourth proportional to 189, 273 and 153?

Options

A. 117
B. 299
C. 221
D. 187

Answer

To find the fourth proportional to the numbers 189, 273, and 153, we can follow these steps:

### Step 1: Set up the proportion
We denote the fourth proportional as \( X \). According to the definition of the fourth proportional, we can set up the equation as follows:
\[ \frac{189}{273} = \frac{153}{X} \]

### Step 2: Cross-multiply
To eliminate the fraction, we cross-multiply:
\[ 189 \cdot X = 273 \cdot 153 \]

### Step 3: Calculate \( 273 \cdot 153 \)
Now, we need to calculate the right side of the equation:
\[ 273 \cdot 153 \]
Calculating this gives:
\[ 273 \cdot 153 = 41889 \]

### Step 4: Substitute back into the equation
Now substitute this value back into our equation:
\[ 189 \cdot X = 41889 \]

### Step 5: Solve for \( X \)
To find \( X \), divide both sides by 189:
\[ X = \frac{41889}{189} \]

### Step 6: Perform the division
Now, we perform the division:
\[ X = 221 \]

Thus, the fourth proportional to 189, 273, and 153 is \( \boxed{221} \).

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