Two vertical poles of height, 20m and 80m stand apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top  of each pole to the foot of the other, from this horizontal plane is: 

  • Option 1)

    15

  • Option 2)

    18

  • Option 3)

    12

  • Option 4)

    16

 

Answers (1)

Eq.\: of\: AC=\frac{x}{a}+\frac{y}{20}=1\cdots (1)

Eq.\: of\: BD=\left ( y-0 \right )=\frac{80-0}{a-0}\left ( x-0 \right )

=ay=80x\cdots (2)

From (1) and (2) 

\frac{ay}{80\cdot a}+\frac{y}{20}=1\Rightarrow y\left ( \frac{1}{80}+\frac{1}{20} \right )=1

y=16.


Option 1)

15

Option 2)

18

Option 3)

12

Option 4)

16

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