Find the third proportional of 3 and 27.

Options

A. 243
B. 256
C. 289
D. 225

Explanation

To find the third proportional of the numbers 3 and 27, we can follow these steps:

### Step 1: Understand the concept of third proportional
The third proportional to two numbers \( a \) and \( b \) is a number \( x \) such that the ratio of \( a \) to \( b \) is the same as the ratio of \( b \) to \( x \). This can be expressed as:
\[ \frac{a}{b} = \frac{b}{x} \]

### Step 2: Assign the values
In our case, let \( a = 3 \) and \( b = 27 \). We need to find \( x \).

### Step 3: Set up the equation
Using the definition of third proportional, we can write:
\[ \frac{3}{27} = \frac{27}{x} \]

### Step 4: Cross-multiply
Cross-multiplying gives us:
\[ 3 \cdot x = 27 \cdot 27 \]

### Step 5: Calculate \( 27 \cdot 27 \)
Calculating the right side:
\[ 27 \cdot 27 = 729 \]
So, we have:
\[ 3x = 729 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 3 to solve for \( x \):
\[ x = \frac{729}{3} = 243 \]

### Final Answer
Thus, the third proportional of 3 and 27 is \( 243 \).

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