Find the 4th proportional to 4, 16 and 7.

Options

A. 28
B. 29
C. 22
D. 25

Answer

To find the 4th proportional to the numbers 4, 16, and 7, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Proportions**:
The 4th proportional to the numbers A, B, and C is a number D such that the ratio A:B is equal to C:D. In this case, we have:
- A = 4
- B = 16
- C = 7
- D = X (the value we need to find)

2. **Set Up the Proportion**:
We can express the relationship as:
\[ \frac{A}{B} = \frac{C}{D} \]
Substituting the known values:
\[ \frac{4}{16} = \frac{7}{X} \]

3. **Cross-Multiply**:
To eliminate the fractions, we cross-multiply:
\[ 4 \cdot X = 16 \cdot 7 \]

4. **Calculate the Right Side**:
Now, calculate \(16 \cdot 7\):
\[ 16 \cdot 7 = 112 \]
So, we have:
\[ 4X = 112 \]

5. **Solve for X**:
To find X, divide both sides by 4:
\[ X = \frac{112}{4} \]
Calculating this gives:
\[ X = 28 \]

6. **Conclusion**:
Therefore, the 4th proportional to 4, 16, and 7 is:
\[ \boxed{28} \]