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

Given:
XY ∥ QR
\(\dfrac{PQ}{XQ} = \dfrac{7}{3}\)
PR = 6.3 cm

Since XY ∥ QR, the Basic Proportionality Theorem applies:
\[ \frac{PX}{PQ} = \frac{PY}{PR} \]
From the given ratio:
\[ \frac{PQ}{XQ} = \frac{7}{3} \] Let PQ = 7k and XQ = 3k.
Then:
\[ XQ = PQ - PX \Rightarrow 3k = 7k - PX \] \[ PX = 4k \]
So the ratio becomes:
\[ \frac{PX}{PQ} = \frac{4k}{7k} = \frac{4}{7} \]
By similarity of triangles PXY and PQR:
\[ \frac{PY}{PR} = \frac{4}{7} \]
Substitute PR = 6.3 cm:
\[ PY = \frac{4}{7} \times 6.3 \] \[ PY = 3.6\ \text{cm} \]
Now find YR:
\[ YR = PR - PY \] \[ YR = 6.3 - 3.6 = 2.7\ \text{cm} \]

Final Answer:
\[ \boxed{YR = 2.7\ \text{cm}} \]