question_answer

Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m, what is the distance between their tops?

A) 13 m

B)  14 m   

C)  15 m   

D)  12.8 m

Correct Answer: A

Solution :

Let AB and CD be the poles such that

AB = 6 m, CD = 11 m and BD = 12 m

Draw \[AE\bot CD.\]Then, AE = BD = 12 m

\[CE=CD-DE=CD-AB=(11-6)m=5\,\,\text{m}\]

From right \[\Delta AEC,\]we have

\[A{{C}^{2}}=A{{E}^{2}}+C{{E}^{2}}={{(12)}^{2}}+{{5}^{2}}=(144+25)=169\]

\[\therefore \]      \[AC=\sqrt{169}=13\,\,\text{cm}\]

Distance between their tops = 13 m