What is the third proportional to `16` and `24` ?

Options

A. A)`28`
B. B)`34`
C. C)`32`
D. D)`36`

Answer

To find the third proportional to the numbers 16 and 24, we can follow these steps:

### Step 1: Understand the Concept of Proportionality
The third proportional to two numbers A and B is a number C such that the ratio of A to B is equal to the ratio of B to C. In mathematical terms, this can be expressed as:
\[ \frac{A}{B} = \frac{B}{C} \]

### Step 2: Assign Values
In our case, let:
- A = 16
- B = 24
- C = K (the third proportional we want to find)

### Step 3: Set Up the Proportionality Equation
Using the proportionality concept, we can set up the equation:
\[ \frac{16}{24} = \frac{24}{K} \]

### Step 4: Cross-Multiply to Solve for K
Cross-multiplying gives us:
\[ 16 \cdot K = 24 \cdot 24 \]
This simplifies to:
\[ 16K = 576 \]

### Step 5: Solve for K
Now, divide both sides by 16 to isolate K:
\[ K = \frac{576}{16} \]
Calculating this gives:
\[ K = 36 \]

### Conclusion
Thus, the third proportional to 16 and 24 is **36**.

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