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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.

5.  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.
 

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As we can see the tree makes a right angle with 

Perpendicular = 5 m

Base = 12 m

As we know, 

In a Right-angled Triangle: By Pythagoras Theorem,

(Hypotenus)^2=(Base)^2+(Perpendicular)^2

(Hypotenus)^2=(12)^2+(5)^2

(Hypotenus)^2=144+25

(Hypotenus)^2=169

Hypotenus=13

Here, The Hypotenuse of the triangle was also a part of the tree originally, So

The Original height of the tree = height + hypotenuse 

                                                 = 5 m + 13 m 

                                                 = 18 m.

Hence the original height of the tree was 18 m.

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