question_answer

A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.

A)  \[20\,m\]                     

B)  \[36\,m\]         

C)         \[18\,m\]                     

D)         \[25\,m\]         

Correct Answer: C

Solution :

Let KB is original height of the tree. In  \[\Delta ABC,\]                         \[A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}=52+122\]       \[=25+144=169\] \[\therefore \]   \[AC=\sqrt{169}=13\,m\] \[KB=KA+AB\] \[=(13+5)\,m=\,18m\]                \[\therefore \]  Original height of the tree is 18m.