In the given figure, \(XY \parallel QR\), \(\frac{PQ}{XQ} = \frac{7}{3}\) and \(PR = 6.3 \text{ cm}\). Find the length of \(YR\).
Show 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.
We are given:
XY ∥ QR, and PQ/XQ = 7/3.
PR = 6.3 cm.
Using the properties of similar triangles, since XY ∥ QR, triangle PXY is similar to triangle PQR.
The ratio of corresponding sides is the same.
Therefore,
\[
\frac{PQ}{XQ} = \frac{PR}{YR}
\]
Given that \( \frac{PQ}{XQ} = \frac{7}{3} \) and \( PR = 6.3 \) cm, we can use this to find YR.
Let the length of YR be \( x \). Then:
\[
\frac{7}{3} = \frac{6.3}{x}
\]
Cross-multiply:
\[
7x = 6.3 \times 3
\]
\[
7x = 18.9
\]
\[
x = \frac{18.9}{7} = 2.7 \text{ cm}
\]
Final Answer:
The length of YR is
\[
\boxed{2.7 \text{ cm}}
\]
