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Two vertical poles of height 9 m and 14 m stand on a plane ground. If the distance between their feet is 12 m, then the distance between their tops is,

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10 m

11 m

12 m

13 m

answer is D.

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Detailed Solution

Given that,
Two vertical poles of height 9 m and 14 m stand on a plane ground.
Consider the figure,
Question Image

Let BC and AD(=BE) represent the two poles of height 14 m and 9 m , respectively.
Let CD be the distance between the tops of the poles.

C E = B C − A D ⇒ C E = 14 − 9 ⇒ C E = 5 m

The Pythagoras theorem is given as,

H y p o t e n u s e 2 = B a s e 2 + P e r p e n d i c u l a r 2

Therefore,

{(DC)}^{2} = {(CE)}^{2} + {(ED)}^{2}

\Rightarrow {(DC)}^{2} = 25 + 144

{\Rightarrow (DC)}^{2} = 169

\Rightarrow DC = 13 m

The distance between the tops of the poles is

13

m.
Hence, option 4 is correct.

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