What is the fourth proportional to 6, 24 and 83?

Options

A. 249
B. 332
C. 166
D. 498

Answer

To find the fourth proportional to the numbers 6, 24, and 83, we can use the concept of proportionality. The fourth proportional \( x \) to the numbers \( a, b, c \) is defined such that:

\[ \frac{a}{b} = \frac{c}{x} \]

In our case, \( a = 6 \), \( b = 24 \), and \( c = 83 \). Therefore, we can set up the equation as follows:

\[ \frac{6}{24} = \frac{83}{x} \]

Now, let's solve for \( x \).

### Step 1: Simplify the left side of the equation

\[ \frac{6}{24} = \frac{1}{4} \]

### Step 2: Set up the equation with the simplified ratio

Now we have:

\[ \frac{1}{4} = \frac{83}{x} \]

### Step 3: Cross-multiply to solve for \( x \)

Cross-multiplying gives us:

\[ 1 \cdot x = 4 \cdot 83 \]

### Step 4: Calculate \( 4 \cdot 83 \)

Calculating this gives:

\[ x = 332 \]

### Conclusion

Thus, the fourth proportional to 6, 24, and 83 is \( \boxed{332} \).

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