The Ist. 3rd and 4th terms of a proportion are 12, 8 and 14 respectively. Find the 2nd term.

Answer

To solve the problem step by step, we will use the concept of proportions.

### Step 1: Understand the problem
We are given three terms of a proportion: the first term (a) is 12, the third term (c) is 8, and the fourth term (d) is 14. We need to find the second term (b).

### Step 2: Set up the proportion
In a proportion, the relationship can be expressed as:
\[ \frac{a}{b} = \frac{c}{d} \]
Substituting the known values, we have:
\[ \frac{12}{b} = \frac{8}{14} \]

### Step 3: Cross-multiply
To eliminate the fractions, we will cross-multiply:
\[ 12 \cdot 14 = 8 \cdot b \]

### Step 4: Calculate the left side
Now, calculate \(12 \cdot 14\):
\[ 12 \cdot 14 = 168 \]
So, we have:
\[ 168 = 8 \cdot b \]

### Step 5: Solve for b
To find \(b\), divide both sides by 8:
\[ b = \frac{168}{8} \]

### Step 6: Perform the division
Now, calculate \( \frac{168}{8} \):
\[ b = 21 \]

### Conclusion
The second term of the proportion is \(21\).

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