Question

Three parallel lines are cut by two transversals as shown in the given figure. If AB = 2 cm, BC = 4 cm and DE = 1.5 cm, then the length of EF is:

• A. 2 cm
• B. 3 cm
• C. 3.5 cm
• D. 4 cm

Hint:

Three parallel lines cut two transversals in the same ratio: AB/BC = DE/EF.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept.
Three parallel lines cut two transversals proportionally, so the ratio of segments on one transversal must equal the ratio of the corresponding segments on the other transversal.

Step 2: Find the ratio on the first transversal.
On the transversal through A, B, C: \(\dfrac{AB}{BC}=\dfrac{2}{4}=\dfrac{1}{2}\).

Step 3: Apply the same ratio to the second transversal.
On the transversal through D, E, F, the same ratio must hold: \(\dfrac{DE}{EF}=\dfrac{1}{2}\).

Step 4: Solve for EF.
Since DE = 1.5 cm and \(\dfrac{DE}{EF}=\dfrac{1}{2}\), EF must be twice DE: \(EF=2\times1.5=3\) cm.

Step 5: Final Answer.
EF is 3 cm, so option B is correct.