7th Class
Mathematics
The Triangle and its Properties
Question Bank
The Triangle and Its Properties
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.