Question : The top of a broken tree touches the ground at a distance of 15 metres from its base. If the tree is broken at a height of 8 metres from the ground, then the actual height of the tree is:
Option 1: 17 metres
Option 2: 20 metres
Option 3: 25 metres
Option 4: 30 metres
Correct Answer: 25 metres
Solution :
Given: The top of a broken tree touches the ground at a distance of 15 metres from its base and the tree is broken at a height of 8 metres from the ground.
Let h be the actual height of the tree.
From the figure we get,
BD = 8 metres, BC = 15 metres and AD = CD = (h – 8) metres.
By using the Pythagoras theorem,
CD
2
= BD
2
+ BC
2
⇒ (h – 8)
2
= 8
2
+ 15
2
⇒ (h – 8)
2
= 289
⇒ (h – 8) = 17
⇒ h = 17 + 8
⇒ h = 25
Hence, the correct answer is 25 metres.
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