Question

In the given figure, if PX-5 cm, XR = 3 cm, QR-7.2 cm and XY || PQ, then the length of RY is 

• A. 2.7 cm
• B. 3 cm
• C. 2.9 cm
• D. Cannot be determined

Answer 1

The Correct Option is A

We are tasked with finding the length of \( RY \) in the given figure, where \( XY \parallel PQ \), \( PX = 5 \, \text{cm} \), \( XR = 3 \, \text{cm} \), and \( QR = 7.2 \, \text{cm} \).

Step 1: Use the Basic Proportionality Theorem (BPT).

The Basic Proportionality Theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. Here, \( XY \parallel PQ \), so:

\[ \frac{PX}{XR} = \frac{QY}{RY}. \]

Step 2: Substitute the known values.

From the problem, \( PX = 5 \, \text{cm} \), \( XR = 3 \, \text{cm} \), and \( QR = QY + RY = 7.2 \, \text{cm} \). Let \( RY = x \), so \( QY = 7.2 - x \). Substituting into the proportion:

\[ \frac{PX}{XR} = \frac{QY}{RY} \implies \frac{5}{3} = \frac{7.2 - x}{x}. \]

Step 3: Solve for \( x \).

Cross-multiply to eliminate the fractions:

\[ 5x = 3(7.2 - x). \]

Expand the terms:

\[ 5x = 21.6 - 3x. \]

Rearrange to isolate \( x \):

\[ 5x + 3x = 21.6 \implies 8x = 21.6 \implies x = \frac{21.6}{8} = 2.7 \, \text{cm}. \]

Final Answer: The length of \( RY \) is \( \mathbf{2.7 \, \text{cm}} \), which corresponds to option \( \mathbf{(1)} \).