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:

You can use the full-side ratio directly: \(\frac{\text{Total Side}}{\text{Segment}} = \frac{\text{Total Side}}{\text{Segment}}\). This saves the step of subtracting parts from the whole.

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: Key Formula or Approach:
Since \(XY \parallel QR\), then \(\frac{PX}{XQ} = \frac{PY}{YR}\) or \(\frac{PQ}{XQ} = \frac{PR}{YR}\).
Step 3: Detailed Explanation:
Given: \(\frac{PQ}{XQ} = \frac{7}{3}\) and \(PR = 6.3 \text{ cm}\).
Using the ratio property of parallels:
\[ \frac{PQ}{XQ} = \frac{PR}{YR} \]
Substitute the given values:
\[ \frac{7}{3} = \frac{6.3}{YR} \]
Cross-multiply to find \(YR\):
\[ 7 \cdot YR = 3 \cdot 6.3 \]
\[ 7 \cdot YR = 18.9 \]
\[ YR = \frac{18.9}{7} \]
\[ YR = 2.7 \text{ cm} \]
Step 4: Final Answer:
The length of \(YR\) is 2.7 cm.