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:
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:
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Three parallel lines cut two transversals in the same ratio: AB/BC = DE/EF.
Updated On: Jul 15, 2026
- 2 cm
- 3 cm
- 3.5 cm
- 4 cm
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept.
When three parallel lines are cut by two transversals, they divide both transversals in the same ratio (the basic proportionality / intercept theorem). Here AD, BE and CF are parallel (the three horizontal lines), and the transversals are cut proportionally.
Step 2: Set up the proportion.
\(\dfrac{AB}{BC}=\dfrac{DE}{EF}\).
Step 3: Substitute the known values.
\(\dfrac{2}{4}=\dfrac{1.5}{EF}\).
Step 4: Solve for EF.
\(EF=\dfrac{1.5\times4}{2}=\dfrac{6}{2}=3\) cm.
Step 5: Final Answer.
EF is 3 cm, so option B is correct.
When three parallel lines are cut by two transversals, they divide both transversals in the same ratio (the basic proportionality / intercept theorem). Here AD, BE and CF are parallel (the three horizontal lines), and the transversals are cut proportionally.
Step 2: Set up the proportion.
\(\dfrac{AB}{BC}=\dfrac{DE}{EF}\).
Step 3: Substitute the known values.
\(\dfrac{2}{4}=\dfrac{1.5}{EF}\).
Step 4: Solve for EF.
\(EF=\dfrac{1.5\times4}{2}=\dfrac{6}{2}=3\) cm.
Step 5: Final Answer.
EF is 3 cm, so option B is correct.
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