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

To solve the problem, we need to use the Basic Proportionality Theorem (also known as Thales' theorem). This theorem states that if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the other two sides are divided in the same ratio.

In the given figure, \(EA \parallel SR\). Therefore, by the Basic Proportionality Theorem:

\(\frac{PE}{ES} = \frac{PA}{AR}\)

Given:

• \(PE = x\) cm
• \(ES = 1.8\) cm
• \(PA = 2\) cm
• \(AR = 1.5\) cm

Substitute these values into the proportion:

\(\frac{x}{1.8} = \frac{2}{1.5}\)

Cross multiply to find \(x\):

\(x \times 1.5 = 2 \times 1.8\)

\(1.5x = 3.6\)

Divide both sides by 1.5:

\(x = \frac{3.6}{1.5} = 2.4\) cm

Now, we need to find the value of \(5x\):

\(5x = 5 \times 2.4 = 12\) cm

Thus, the solution is 12 cm.