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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Solution

In the given figure, BC represents the unbroken part of the tree. Point C represents the point where the tree broke and CA represents the broken part of the tree. Triangle ABC, thus formed, is right-angled at B.

Applying Pythagoras theorem in ΔABC,

AC² = BC² + AB²

AC² = (5 m)² + (12 m)²

AC² = 25 m² + 144 m² = 169 m²

AC = 13 m

Thus, original height of the tree = AC + CB = 13 m + 5 m = 18 m

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Q. 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.

Question 11

The top of a broken tree touches the ground at a distance of 12 m from its base. If the tree is broken at a height of 5 m from the ground, then the actual height of the tree is
a) 25 m
b) 13 m
c) 18 m
d) 17 m

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