Question

In the given figure, \( XY \parallel QR \), \( \frac{PQ}{XQ} = \frac{7}{3} \) and \( PR = 6.3 \text{ cm} \). Find the length of \( YR \).

Hint:

If the full length of a side is given, use the full-side to partial-side ratio directly to save time.

Answer 1

Step 1: Understanding the Concept:
By the Basic Proportionality Theorem (BPT), if a line is drawn parallel to one side of a triangle, it divides the other two sides in the same ratio.
Step 2: Detailed Explanation:
Since \( XY \parallel QR \), by BPT:
\[ \frac{PX}{XQ} = \frac{PY}{YR} \]
Adding 1 to both sides leads to the corollary:
\[ \frac{PX + XQ}{XQ} = \frac{PY + YR}{YR} \implies \frac{PQ}{XQ} = \frac{PR}{YR} \]
Given \( \frac{PQ}{XQ} = \frac{7}{3} \) and \( PR = 6.3 \text{ cm} \):
\[ \frac{7}{3} = \frac{6.3}{YR} \]
\[ YR = \frac{6.3 \times 3}{7} \]
\[ YR = 0.9 \times 3 = 2.7 \text{ cm} \]
Step 3: Final Answer:
The length of YR is 2.7 cm.