# 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.

P Pankaj Sanodiya

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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