s at t are transversals cutting a set of parallel lines such that a segment of length 3 in s corresponds to a segment of length 5 in t. What is the length of segment in t corresponding to a segment of length 12 in s ?

Options

A. 20
B. `(36)/(5)`
C. 14
D. `(5)/(4)`

Answer

To solve the problem, we need to establish the relationship between the lengths of segments in the two transversals (s and t) that cut across the parallel lines. We know that the segments are proportional.

### Step-by-Step Solution:

1. **Identify the Known Values:**
- Length of segment in s (S1) = 3
- Length of corresponding segment in t (T1) = 5
- Length of another segment in s (S2) = 12
- Length of the corresponding segment in t (T2) = ?

2. **Set Up the Proportional Relationship:**
Since the segments are proportional, we can write the relationship as:
\[ \frac{S1}{S2} = \frac{T1}{T2} \]

3. **Substitute the Known Values:**
Plugging in the known values into the equation:
\[ \frac{3}{12} = \frac{5}{T2} \]

4. **Cross Multiply to Solve for T2:**
Cross multiplying gives us:
\[ 3 \cdot T2 = 12 \cdot 5 \]
Simplifying the right side:
\[ 3 \cdot T2 = 60 \]

5. **Divide Both Sides by 3:**
To isolate T2, divide both sides by 3:
\[ T2 = \frac{60}{3} = 20 \]

6. **Conclusion:**
The length of the segment in t corresponding to a segment of length 12 in s is:
\[ T2 = 20 \]

### Final Answer:
The length of the segment in t corresponding to a segment of length 12 in s is **20**.

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