If a line is divided by three parallel lines into two-segments of lengths in the ratio 1 : 3, another line will be divided by these parallel lines into two segments of lengths in the ratio

1 : 3

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3 : 1

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1 : 2

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2 : 1

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Solution

The correct option is A 1 : 3
$I n t r i a n g l e A B O a n d A C D B O ∥ C D S o △ A B O \sim △ A C D \frac{A B}{A C} = \frac{A O}{O D} \frac{A O}{O D} = \frac{1}{3} . . . . . . (1) N o w i n t r i a n g l e D E O a n d D F E E O ∥ A F S o △ D E O \sim △ D F E \frac{D E}{E F} = \frac{D O}{O A} = \frac{3}{1} U s i n g e q u a t i o n . . . . . . (1) H e n c e \frac{E F}{D E} = \frac{1}{3}$ \\

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If a line is divided by three parallel lines into two-segments of lengths in the ratio 1 : 3, another line will be divided by these parallel lines into two segments of lengths in the ratio

The correct option is A 1 : 3IntriangleABOandACDBO∥CDSo△ABO∼△ACDABAC=AOODAOOD=13......(1)NowintriangleDEOandDFEEO∥AFSo△DEO∼△DFEDEEF=DOOA=31Usingequation......(1)HenceEFDE=13\\