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Mathematics

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

A
1 : 3
B
3 : 1
C
1 : 2
D
2 : 1
Answer & Solution

1 : 3


SOLUTION
$$\quad In\quad triangle\quad ABO\quad and\quad ACD\\ BO\quad \parallel \quad CD\\ So\quad \triangle ABO\quad \sim \quad \triangle ACD\\ \frac { AB }{ AC } \quad =\quad \frac { AO }{ OD } \\ \frac { AO }{ OD } \quad =\quad \frac { 1 }{ 3 } ......(1)\\ Now\quad in\quad triangle\quad DEO\quad and\quad DFE\\ EO\quad \parallel \quad AF\\ So\quad \triangle DEO\quad \sim \quad \triangle DFE\\ \frac { DE }{ EF } \quad =\quad \frac { DO }{ OA } \quad =\quad \frac { 3 }{ 1 } \quad \quad Using\quad equation\quad ......(1)\\ Hence\quad \frac { EF }{ DE } \quad =\quad \frac { 1 }{ 3 } $$\\ 
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