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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


Team Careers360 20th Jan, 2024
Answer (1)
Team Careers360 21st Jan, 2024

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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