question_answer

Two poles of height \[13\,m\] and \[7\,m\] respectively stand vertically on a plane ground at a distance of \[8\,m\] from each other. The distance between their tops is:

A) \[9\,m\]

B) \[10\,m\]

C) \[11\,m\]

D) \[12\,m\]

Correct Answer: B

Solution :

[b] Let AB and CD be the poles such that \[AB=13\,m,\] \[CD=7\,m\]

and \[CA=8m.\]

Draw \[DE\bot AB\].

Then, \[AE=CD=7m,\] \[BE=6m\]

and   \[DE=8m.\]

In right \[\Delta BDE,\] by Pythagoras theorem

\[B{{D}^{2}}=B{{E}^{2}}+D{{E}^{2}}={{6}^{2}}+{{8}^{2}}\]

\[=36+64=100\]

\[\Rightarrow \,\,\,\,\,\,\,\,BD=\sqrt{100}=10m.\]

Hence, the distance between their tops is \[10m\].