Find the fourth proportional to :
4, 9, 32

Answer

To find the fourth proportional to the numbers 4, 9, and 32, we can follow these steps:

### Step 1: Understand the concept of proportionality
We need to find a number \( x \) such that the ratio of the first two numbers (4 and 9) is the same as the ratio of the last two numbers (32 and \( x \)). This can be expressed as:
\[ \frac{4}{9} = \frac{32}{x} \]

### Step 2: Set up the equation
Cross-multiply to set up the equation:
\[ 4 \cdot x = 9 \cdot 32 \]

### Step 3: Calculate the right side of the equation
Now, calculate \( 9 \cdot 32 \):
\[ 9 \cdot 32 = 288 \]

### Step 4: Substitute back into the equation
Now substitute this value back into the equation:
\[ 4x = 288 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides of the equation by 4:
\[ x = \frac{288}{4} \]

### Step 6: Perform the division
Now perform the division:
\[ x = 72 \]

### Conclusion
Thus, the fourth proportional to 4, 9, and 32 is \( 72 \).

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