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: Use Basic Proportionality Theorem
Since XY ∥ QR,
the sides are divided in the same ratio.

So,
PQ / XQ = PR / YR

Step 2: Substitute Given Values
Given:
PQ / XQ = 7/3
PR = 6.3 cm

So,
7/3 = 6.3 / YR

Step 3: Solve for YR
Cross multiply:
7 × YR = 3 × 6.3

7 × YR = 18.9

YR = 18.9 / 7
YR = 2.7 cm

Final Answer:
Length of YR = 2.7 cm