Question

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

Hint:

Using the ratio \( \frac{\text{Total Side}}{\text{Segment}} \) directly can often save time compared to finding intermediate segment lengths.

Answer 1

Step 1: Understanding the Concept:
According to 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. Also, using properties of ratios, we can find parts of segments.
Step 2: Key Formula or Approach:
If \( XY || QR \), then \( \frac{PX}{XQ} = \frac{PY}{YR} \) or \( \frac{PQ}{XQ} = \frac{PR}{YR} \).
Step 3: Detailed Explanation:
Given: \( \frac{PQ}{XQ} = \frac{7}{3} \).
Since \( XY || QR \), the segments are proportional:
\[ \frac{PQ}{XQ} = \frac{PR}{YR} \]
Substitute the given values \( \frac{PQ}{XQ} = \frac{7}{3} \) and \( PR = 6.3 \):
\[ \frac{7}{3} = \frac{6.3}{YR} \]
\[ 7 \times YR = 3 \times 6.3 \]
\[ 7 \times YR = 18.9 \]
\[ YR = \frac{18.9}{7} \]
\[ YR = 2.7 \text{ cm} \]
Step 4: Final Answer:
The length of YR is 2.7 cm.