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A tree is broken at a height of $8$ m from the ground and its top touches the ground at a distance of $15$ m from the base of the tree. Find the original height of the tree.

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25 m

5 m

23 m

16 m

answer is A.

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Detailed Solution

Given that a tree is broken at a height of

8

m from the ground and its top touches the ground at a distance of

15

m from the base of the tree.
Question Image

Let

BD

be the original height of tree.

∴ AD = AC

So,
AB=8m
BC=15m
In

△ ABC,

by the pythagoras theorem,

A C^{2} = {BC}^{2} + {AB}^{2}

\Rightarrow A C^{2} = 15^{2} + 8^{2}

\Rightarrow A C^{2} = 225 + 64

\Rightarrow A C^{2} = 289

\Rightarrow AC = 17 m

\Rightarrow AD = 17 m

∴

Original height of tree

= (17 + 8) m = 25 m

.
Thus, the original height of the tree is 25m.
Therefore, the correct option is 1.

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