Question

In the adjoining figure, if \(EA \parallel SR\) and \(PE = x\) cm, then the value of \(5x\) is :

• A. 2.4 cm
• B. 12 cm
• C. 1.35 cm
• D. 6.75 cm

Hint:

Read the final question carefully! Many students stop after finding \(x\), but here you were specifically asked for \(5x\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
According to the Basic Proportionality Theorem (Thales Theorem), if a line is drawn parallel to one side of a triangle to intersect the other two sides, the other two sides are divided in the same ratio.
Step 2: Key Formula or Approach:
\[ \frac{PE}{ES} = \frac{PA}{AR} \]
Step 3: Detailed Explanation:
Assuming a standard figure where \(PE=x, ES=3, PA=2, AR=2.5\):
1. Apply the ratio:
\[ \frac{x}{3} = \frac{2}{2.5} \] 2. Solve for \(x\):
\[ x = \frac{2 \times 3}{2.5} = \frac{6}{2.5} = 2.4 \text{ cm} \] 3. The question asks for the value of \(5x\):
\[ 5x = 5 \times 2.4 = 12 \text{ cm} \]
Step 4: Final Answer:
The value of \(5x\) is 12 cm.