In the given figure, XY || QR, PQ/XQ=7/3 and PR = 6.3 cm, find YR

Answer

To solve the problem, we will follow these steps:

1. **Understand the Given Information**: We have two parallel lines XY and QR, and we know the ratio of segments PQ and XQ, which is given as \( \frac{PQ}{XQ} = \frac{7}{3} \). We also know the length of segment PR, which is 6.3 cm. We need to find the length of segment YR.

2. **Assign Variables**: Let's denote the length of YR as \( x \).

3. **Apply Thales' Theorem**: According to Thales' theorem, if two lines are parallel, then the ratios of the segments created by those lines are equal. Therefore, we can set up the equation:
\[ \frac{PQ}{XQ} = \frac{PR}{YR} \]
Substituting the known values, we have:
\[ \frac{7}{3} = \frac{6.3}{x} \]

4. **Cross-Multiply to Solve for x**: We can cross-multiply to solve for \( x \):
\[ 7x = 3 \times 6.3 \]

5. **Calculate the Right Side**: Now, calculate \( 3 \times 6.3 \):
\[ 3 \times 6.3 = 18.9 \]
So, we have:
\[ 7x = 18.9 \]

6. **Divide by 7**: To find \( x \), divide both sides by 7:
\[ x = \frac{18.9}{7} \]

7. **Perform the Division**: Now, calculate \( \frac{18.9}{7} \):
\[ x = 2.7 \]

8. **Conclusion**: Therefore, the length of YR is \( 2.7 \) cm.

### Final Answer:
YR = 2.7 cm

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