question_answer

Two 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  ;

A)  13m   

B)         12m   

C)         14 m  

D)         15 m              

Correct Answer: A

Solution :

Let AB and CD be the heights of given poles, BC be the distance between their feet and AD be the distance between their tops. Since, BCDE is a rectangle.                         \[\therefore \]  \[EB=DC=9\,m\] and \[ED=BC=12\,m\] \[AE=AB-EB=14\text{ }m-9\text{ }m=5\text{ }m\] Now, \[\Delta AED\]is a right angled triangle \[\therefore \] \[A{{D}^{2}}=A{{E}^{2}}+E{{D}^{2}}\] [By Pythagoras theorem] \[\Rightarrow \] \[A{{D}^{2}}={{(5)}^{2}}+{{(12)}^{2}}=169\Rightarrow AD=13m\] Hence, the distance between their tops is 13 m.