Find the fourth proportional of 4, 9 and 12.

Answer

To find the fourth proportional of the numbers 4, 9, and 12, we will follow these steps:

### Step 1: Understand the concept of fourth proportional
The fourth proportional of three numbers a, b, and c is a number d such that the ratio of a to b is the same as the ratio of c to d. This can be represented as:
\[ \frac{a}{b} = \frac{c}{d} \]

### Step 2: Set up the equation
In our case, we have:
- a = 4
- b = 9
- c = 12
- d = z (the fourth proportional we need to find)

So we can write:
\[ \frac{4}{9} = \frac{12}{z} \]

### Step 3: Cross-multiply to solve for z
Cross-multiplying gives us:
\[ 4 \cdot z = 9 \cdot 12 \]

### Step 4: Calculate the right side
Now calculate \( 9 \cdot 12 \):
\[ 9 \cdot 12 = 108 \]

### Step 5: Substitute back into the equation
Now we have:
\[ 4z = 108 \]

### Step 6: Solve for z
To find z, divide both sides by 4:
\[ z = \frac{108}{4} \]

### Step 7: Simplify the division
Now simplify \( \frac{108}{4} \):
\[ z = 27 \]

### Conclusion
Thus, the fourth proportional of 4, 9, and 12 is:
\[ \text{Fourth Proportional} = 27 \]

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