What is the `4^(th)` proportional of 3,8,12,?
A. 36
B. 26
C. 32
D. 16

Options

A. A
B. C
C. B
D. D

Answer

To find the fourth proportional of the numbers 3, 8, and 12, we can use the property of proportions. The fourth proportional \( x \) can be determined using the following relationship:

If \( a, b, c, \) and \( d \) are in proportion, then:
\[ \frac{a}{b} = \frac{c}{d} \]
From this, we can derive that:
\[ d = \frac{b \cdot c}{a} \]

In our case, we have:
- \( a = 3 \)
- \( b = 8 \)
- \( c = 12 \)
- \( d = x \) (the fourth proportional we want to find)

Now, substituting the values into the formula:
\[ x = \frac{b \cdot c}{a} = \frac{8 \cdot 12}{3} \]

Calculating this step-by-step:
1. First, multiply \( b \) and \( c \):
\[ 8 \cdot 12 = 96 \]

2. Next, divide the result by \( a \):
\[ x = \frac{96}{3} = 32 \]

Thus, the fourth proportional \( x \) is \( 32 \).

### Final Answer:
The fourth proportional of 3, 8, and 12 is \( 32 \).